Yury Shlyapin played for one club, Dynamo Moskva, throughout his sporting career
from 1950 to 1962. With Dynamo Moskva, he won seven Soviet championships (1955,
1957, 1958 and 1960-1962), was second in 1950, 1953 and 1954 and won bronze in 1952. He also won the Open Italian Cup in 1957 with Dynamo Moskva. Shlyapin was
selected to the Soviet national team from 1952 to 1956. He was seventh at 1952
Olympics, won a gold at the 1953 World Student Games (predecessor to
Universiade) and bronze at 1956 Olympics.
After his sporting career, Shlyapin worked as a diving and water polo official in
Soviet Sport Committee. He had a very brief coaching career, being the
head coach of the Dynamo Moskva water polo team from 1977 to 1978, winning silver
at the 1978 Soviet Championships and being runner-up at the 1977 Soviet Cup. From
1980 to 1982, Shlyapin was an aquatics official on the Moscow Sport Committee and
from 1982 to 1987 worked as an official with Spartak Moskva. In 1987 he was
selected to be a first president of the Spartak Moskva football club, a post which he held until his retirement in 1993.