Uhlmann won the 1954, 1955 and 1958 East Germany Chess Championships, and in 1956 was awarded the International Master title, and later the Grandmaster title in 1959. He was the German Democratic Republic's (GDR) most outstanding player at the Chess Olympiads of 1956–1990, where he made 11 appearances, mostly on . At the 1964 event in Tel Aviv, Israel he scored a combined 15 points out of 18, earning him the individual board one gold medal. In the same year, he won his fourth national championship. An individual bronze medal, for a combined score of 13 points out of 18, followed in 1966 at Havana, Cuba.