Meyer was selected with 24th overall pick in the first round of the 1995 NBA Draft. He was drafted by the Dallas Mavericks who landed him in a trade with Rolando Blackman in the 1992 off-season. The Mavericks were a rebuilding team at the team at the time and they had four Centers on the team throughout the 1995-96 season, so Meyer had to fight for minutes. And he earned himself some good minutes, averaging 17.6 minutes per game in his rookie season. He averaged 5.0 points per game and 4.4 rebounds per game in his rookie campaign. He was seen as inefficient and undersized for his position, but he was a good athletic defender and hustler and he had the intangibles which didn't show up the box score but were valuable in-game. On December 28, 1995 Meyer recorded a career high 13 rebounds in a 103-101 win to the Vancouver Grizzlies. On March 31, 1996 Meyer recorded a season high 14 points in a 115-100 loss to the Portland Trail Blazers.