Savelyev, also spelled as Savelev, Saveliev, or Saveljev, or Savelyeva, is a Russian surname that is derived from the male given name Savely and literally means Savely's. Notable people with the surname include:
- Aleksei Vitalyevich Savelyev, Russian footballer who played for FC Torpedo Moscow and PFC CSKA Moscow
- Andrei Saveliyev, Russian politician and a former member of the Russian State Duma
- Boris Savelev,, Russian photographer
- Dmitry Savelyev (disambiguation), several people
- Gennadi Saveliev, American Ballet Theatre soloist
- Ilya Savelev, Russian volleyball player
- Larissa Saveliev, Russian ballet dancer
- Ludmila Savelyeva, Russian film actress and ballerina
- Oleg Savelyev, Russian politician and deputy defense minister
- Sergey Savelyev (skier) (1948–2005), Russian cross country skier
- Sergey Savelyev, Russian speed skater
- Sergey Vyacheslavovich Savelyev, Russian scientist, evolutionist, paleoneurologist, author of the idea of cerebral sorting
- Viktor Savelyev (1928–2013), Russian surgeon
- Viktor Zakharevich Savelyev (1875–1943), Russian military officer
- Vitaly Savelyev, Russian businessman
