Tatyana Andreyevna Savelyeva (; born 22 May 1947) is a retired Russian backstroke swimmer. She competed in four events at the 1964 and 1968 Summer Olympics and won a bronze medal in the 4 à100 m medley relay in 1964; in other events she did not reach the finals. During her career she set six national records and won five national titles in the 100 m (1964âÂÂ1966) and 200 m backstroke (1967âÂÂ1968).
She graduated from the Saint Petersburg State Polytechnical University. After marriage she changed her last name to Gladysheva ().