Henry Glaß was not related to the other East German ski jumpers with this name, although they all came from the same hometown. Henry Glaß won silver medals at the 1978 Nordic World Championships on the normal hill and in the 1972 Four Hills Tournament. He also won a bronze medal at the 1976 Innsbruck Olympics on the normal hill and at the 1977 Ski Flying World Championships. Glaß later became 1980 East German Champion on the large hill, and in 1981 on the normal hill. He was runner-up on the normal hill in 1975 and 1980 and the large hill in 1977.
After his active career he became a coach. He became assistant coach of the German national team in 1990 until it was revealed, shortly before the 2006 Torino Olympics, that he had previously actively worked for the East German Stasi (Staatssicherheit). He was then suspended from coaching by the German NOC and became a youth coach in his hometown of Klingenthal.