The promotion of Bump Elliott to head coach in 1959 defined a historical era of the University of Michigan Wolverines football through 1968 when he resigned after that season. Michigan was a member of the Big Ten Conference and played its home games at Michigan Stadium during the Elliott years. During the 10 years in which Elliott served as head football coach, Michigan compiled a record of 51–42–2 (.547) and claimed one Big Ten championship, one Rose Bowl victory, and two Chicago Tribune Silver Football awards for the most valuable player in the Big Ten. However, the Wolverines finished higher than third place in the Big Ten only twice.
 The 1964 team compiled a 9–1 record, won the Big Ten championship, defeated Oregon State in the 1965 Rose Bowl, and finished the season ranked No. 4 in both the AP and UPI polls.  Quarterback Bob Timberlake was selected as an All-American and won the 1964 Chicago Tribune Silver Football award.  After losing to Michigan by a 34–7 score in the Rose Bowl, Oregon State coach Tommy Prothro opined that the 1964 Wolverines were "the greatest football team he has ever seen."
 In Elliott's final year as head coach, the 1968 team compiled an 8–2 record (6–1 Big Ten) and was ranked No. 12 in the final AP Poll.  Running back Ron Johnson won the Chicago Tribune Silver Football award and broke Michigan's single-game and single-season rushing records.  Johnson's 347-yard rushing performance against Wisconsin still stands as Michigan's single-game record.  The 1968 team also included a core of young players who became stars in the early years of the Schembechler era.
 Four Michigan football players from the Elliott years have been inducted into the College Football Hall of Fame.  They are Tom Curtis (halfback and defensive back, 1967–1969), Dan Dierdorf (offensive tackle, 1968–1970), Ron Johnson (halfback, 1966–1968), and Jim Mandich (tight end, 1967–1969).  Dierdorf and a fifth player, Tom Mack (tackle, 1963–1965), have been inducted into the Pro Football Hall of Fame.  A sixth, Dave Raimey (halfback, 1960–1962), has been inducted into the Canadian Football Hall of Fame.
 The 1958 Michigan team compiled a 2–6–1 record under 11th-year head coach Bennie Oosterbaan.  On November 14, 1958, before the final two losses of the season had been recorded, Oosterbaan announced that he was resigning effective at the end of the season.  University officials announced that Bump Elliott would succeed Oosterbaan as the head football coach in 1959.  Elliott had played for Michigan under Fritz Crisler and had won the Chicago Tribune Silver Football award in 1947 as the most valuable player in the Big Ten Conference.  Elliott had held several assistant coaching positions since 1948, including a position as the backfield coach at Michigan during the 1957 and 1958 seasons.  At age 33, he became the youngest head coach in the conference.
 Elliott promptly shook up the coaching staff, retaining only two of Oosterbaan's assistants.  He hired three young, new assistant coaches: Jack Fouts from Bowling Green, Jack "Jocko" Nelson from Colorado, and Henry Fonde, Elliott's former teammate who was coaching high school football in Ann Arbor.  Predicting that he would require three to five years to rebuild and win a championship, Elliott discarded the single-wing formation that had been the mainstay at Michigan since Fritz Crisler arrived in the late 1930s.  In its place, Elliott installed an offense which he referred to as the "winged-T."
 On September 26, 1959, the Elliott years officially got underway with a home game against the Missouri Tigers.  The Tigers upset the Wolverines, 20–15.  The following week, the Wolverines were again defeated in a home game against Michigan State by a score of 34–8.   The 1959 team finished with a record of 4–5, including victories over rivals Minnesota and Ohio State.  Fred Julian led the 1959 team with 289 rushing yards, and quarterback Stan Noskin led the team in total offense with 697 passing yards.  The 1959 season was regarded as "not bad for a rebuilding year," and the team's 4–5 record was an improvement on the prior two-win season.  A post-season appraisal by the Associated Press referred to the 1959 Wolverines as "resurgent" and "scrappy."  Elliott called it "an encouraging and enjoyable year" and noted that his team was "able to give almost every team we played a real contest."
 In 1960, the team again showed improvement, compiling a 5–4 record and outscoring opponents by a total of 133 to 84. Bennie McRae led the team with 342 rushing yards, and quarterback Dave Glinka totaled 755 passing yards.
 The rebuilding process continued in 1961 as the team improved to a 6–3 record and outscored opponents 212 to 163.  For the first time in the Elliott years, a Michigan player was selected as an All-Big Ten player, with Bennie McRae being picked as an All-Big Ten halfback.  Dave Raimey led the team with 496 rushing yards, and quarterback Dave Glinka added 588 passing yards.
 The steady improvement in the team's record was reversed in 1962, which marked a low point in the Elliott years.  Before the season began, the team lost three of its best offensive players, end John Henderson, fullback Bruce McLenna, and kicker Doug Bickle, to injuries.  The 1962 Michigan team compiled a 2–7 record (1–6 Big Ten), finished dead last in the conference, and was outscored 214 to 70.  The delta of −144 between points scored and points allowed marked the worst performance in the history of Michigan football, exceeding the previous record of −122 set by the 1934 team.  (The 2008 team compiled a −104 delta for third worst in school history.) Dave Raimey led the team with 385 rushing yards, and quarterback Bob Chandler added 401 passing yards.
 The Wolverines continued to struggle in 1963, compiling a 3–4–2 record and finishing in a tie for fifth place in the Big Ten.  In the second game of the season, the Wolverine fell, 26–13, to a Navy team that was ranked No. 6 in the AP Poll and led by Roger Staubach.  Staubach's performance in the game (94 rushing yards and 14 of 16 passing for 237 yards) was called "one of the most remarkable performances in the 36-year history of Michigan Stadium."  The defense improved substantially in 1963, allowing 127 points in nine games, but the offense was limited to 131 points in those same games.  Quarterback Bob Timberlake showed promise with 593 passing yards and 228 rushing yards.  Two Michigan linemen, Tom Keating and Joe O'Donnell, became the second and third Michigan players to be named to All-Big Ten teams during the Elliott years.
 At the end of Elliott's first five years as head coach, Michigan had compiled an overall record of 20–23–2 and finished no higher than fifth place in the Big Ten Conference. No Michigan football players received All-America honors during those years.
 In its sixth year under Bump Elliott, the 1964 Michigan team compiled a 9–1 record and won the Big Ten Conference championship for the first time since 1950.  Although no post-bowl polls were taken in the 1964 season, the Wolverines finished the regular season ranked No. 4 in both the AP and UPI polls.
 In the second game of the season, Michigan avenged its 1963 loss to Navy and 1963 Heisman Trophy winner Roger Staubach.  Navy came into the game ranked No. 5 in the country.  This time, the Wolverines were able to stop Staubach and won the game, 21–0.  Michigan intercepted three Navy passes, including two thrown by Staubach.  Staubach was eventually forced from the game, limping after being knocked to the turf by Michigan defensive tackle Bill Yearby.  The game broke a 20-game streak during which the Midshipmen had not been shut out under Staubach.  The New York Times wrote that the Wolverines "brought Roger Staubach, the heroic middie quarterback, back into focus as an ordinary mortal."
 The 1964 team narrowly missed an undefeated season, with its only loss coming against a Purdue team led by Bob Griese.  The Wolverines lost to Purdue by a score of 21–20.  Michigan had a chance to tie the game in the fourth quarter, but quarterback Bob Timberlake carried the ball for an attempted two-point conversion and was stopped short of the goal line.
 On offense, Timberlake was a triple threat who rushed for 631 yards, passed for 884 yards, and also handled field goals and extra points.  He won the Chicago Tribune Silver Football award as the most valuable player in the conference and was selected as an All-American.  The 1964 team also had a strong running game with Mel Anthony and Carl Ward in the backfield.  The Wolverines rushed for 2,473 yards in 1964 and had four games (Air Force, Minnesota, Northwestern, and Oregon State) in which they rushed for over 300 yards.
 On defense, Michigan registered three shutouts (a feat not accomplished by a Michigan team since 1948) and gave up only 83 points, an average of 8.3 points per game.  Team leaders on defense included All-American defensive tackle Bill Yearby, All-Big Ten linebacker Tom Cecchini, and team captain and All-Big Ten end Jim Conley.
 As the Big Ten champions, the Wolverines advanced to the 1965 Rose Bowl, defeating Oregon State by a score of 34–7.  Michigan fullback Mel Anthony was awarded the Player of the Game trophy after scored three touchdowns, including an 84-yard run in the second quarter that set a Rose Bowl record.  Oregon State coach Tommy Prothro opined after watching game film from the Rose Bowl that the 1964 Wolverines were "the greatest football team he has ever seen."
 After winning a Big Ten championship in 1964, and then opening the 1965 season with two victories, the 1965 team was ranked No. 4 in the AP Poll after two weeks of play.  However, the team was crippled by multiple injuries and lost six of the eight remaining games.  The 1965 team ultimately compiled a 4–6 record and tied for seventh place in the conference.  Carl Ward led the team with 639 rushing yards, and quarterback Wally Gabler passed for 825 yards.
 The 1966 team improved to 6–4 and tied for third place in the conference standings.  The team featured the strongest passing attack in Michigan history to that point.  Quarterback Dick Vidmer shattered Michigan's single-season records by completing 117 of 225 passes for 1,609 yards and 10 touchdowns.  Vidmer's favorite target was Jack Clancy who caught 76 passes for 1,077 yards in 1966.   After starting the season with impressive victories over Oregon State (41–0) and No. 7-ranked  California (17–7), the Wolverines were ranked No. 9 in the AP Poll.  Three straight losses dropped the team out of the national rankings.  In the final game of the season, the Wolverines defeated rival Ohio State, 17–3.  Dave Fisher led the 1966 team with 672 rushing yards.  Two Wolverines were selected as All-Americans in 1966: safety Rick Volk and end Jack Clancy.   A record five Michigan players were selected as All-Big Ten players in 1966: Volk, Clancy, right guard Don Bailey, halfback Jim Detwiler, fullback Dave Fisher, and linebacker Frank Nunley.
 The 1967 team lost five of its first six games, compiled a 4–6 record, and tied for fifth place in the Big Ten standings.  Ron Johnson led the team with 982 rushing yards, while quarterback Dennis Brown led the team in total offense with 928 passing yards and 358 rushing yards.  Center Joe Dayton, linebacker Tom Stincic, and Ron Johnson were  selected as All-Big Ten players in 1967.
 Michigan opened the 1968 season with a disappointing 21–7 loss at home in Ann Arbor to the California Golden Bears.  After the season opener, the team won eight consecutive games, including a 28–14 victory over a Michigan State team that was ranked No. 12 in the AP Poll and a 27–22 victory over an Indiana team that was ranked No. 19 in the AP Poll.  By mid-November, the Wolverines were ranked No. 4 in both the AP and UPI polls.  On November 16, 1968, running back Ron Johnson rushed for 347 yards against Wisconsin, a mark that still stands as Michigan's single-game rushing record.   Johnson rushed for a total of 1,391 yards in 1968, setting a season rushing record that stood until broken by Rob Lytle in 1976.  Quarterback  Dennis Brown added 1,562 passing yards and 215 rushing yards.
 In the final game of the 1968 season, Michigan faced Ohio State.  Michigan came into the game ranked No. 4, and Ohio State was undefeated and ranked No. 2.  Ohio State won the game by a 50–14 score.  Despite having a 36-point lead, Ohio State coach Woody Hayes passed for, and failed to get, a two-point conversion after the final score and with 1:23 remaining in the game.  When asked why he went for the two-point conversion, Hayes reportedly said, "Because we couldn't go for three!"  The 1968 Buckeyes went on to defeat USC in the 1969 Rose Bowl and were recognized as national champions in both the AP and UPI polls.
 The 1968 Michigan team included a core of young players (Dan Dierdorf, Jim Mandich, Don Moorhead, Tom Curtis, Marty Huff,  Henry Hill, and Cecil Pryor) who became stars in the early years of the Schembechler era.
 In late December 1968, Elliott resigned as head coach and accepted a new position as Michigan's associate athletic director. Less than a week later, Bo Schembechler was announced as Elliott's replacement.
 There were reports during the 1968 season that Elliott had been given an ultimatum: "Either win or face the possibility of being kicked upstairs."   Don Canham, who took over as athletic director in 1968, later denied that Elliott was "eased out" of his job.  Canham said: "Bump and I are close personal friends.  Bump is not naïve – he knows that when you work at a place for 10 years and you're not winning consistently, it doesn't become fun for anybody – the coach, the alumni, the players or anybody else.  We talked about this and we talked about it openly.  If Bump had said to me, 'Look, give me a couple of more years,' I would have given it to him.  I mean that.  I didn’t fire Bump Elliott.  My first year as director Bump had an 8 and 2 record.  Anyone could live with that."
 Schembechler later recalled that he remained loyal to Elliott when he took over as Michigan's head coach.  When Schembechler's 1969 team won the Big Ten championship, he said, "I made certain I let everyone know I won with Bump's kids.  Bump was a man of great class and he showed it to me again and again in that first year, never getting in the way, always trying to be helpful, always trying to encourage me."  After Michigan won the 1969 Ohio State game, the team presented the game ball to Elliott, and Schembechler noted that "I don't remember when I felt happier about anything in my life."  After two years as Michigan's associate athletic director, Elliott was hired as Iowa's athletic director in 1970.
 Elliott was the first head coach in Michigan history to compile losing records in all three of Michigan's principal rivalries with Michigan State, Minnesota, and Ohio State.  Elliott compiled an overall record of 9–20–1 in those series.
 During the Elliott years, Michigan compiled a  2–7–1 record in the Michigan – Michigan State football rivalry.  Duffy Daugherty was the head coach of Michigan State throughout the Elliott years.  Significant games during the Elliott-Daugherty years include:
 During the Elliott years, Michigan compiled a 4–6 record in its annual Little Brown Jug rivalry game with the Minnesota Golden Gophers.  Murray Warmath was the head coach at Minnesota throughout the Elliott years.  Significant games during the Elliott-Warmath years include:
 During the Elliott years, Michigan compiled a 3–7 record in the Michigan–Ohio State football rivalry.  Woody Hayes was the head coach at Ohio State throughout the Elliott years.  Significant games during the Elliott-Hayes years include:
 From 1960 to 1966, Michigan's games against Illinois took on heightened significance as the games matched Bump Elliott against his brother Pete Elliott, who was Illinois' head coach.  The Elliott brothers had played together on the undefeated 1947 Michigan Wolverines football team and were both later inducted into the College Football Hall of Fame.  In the seven games matching the two brothers against each other, Michigan compiled a record of 6–1.  In his history of the Michigan football program, former publicity director Will Perry joked about the Elliott years: "Two things were becoming clear about Michigan football.  There would be injuries, and Bump Elliott's team would beat Pete Elliott's Illinois team."
 Michigan and Notre Dame did not play each other during the Elliott years.   After playing against each other in 1942 and 1943, the programs did not meet again until 1978.