He spent eighteen months in the graphic arts department of the Herzen Pedagogical Institute.

In 1965 he graduated from Saint Petersburg State Theatre Arts Academy (Boris Sohn's course).

In his last years he only played in the combination company productions of the theater Comedians.

Some of Kostetskiy's most famous roles were in films directed by Vladimir Vorobyov: Wedding of Krechinsky, Truffaldino from Bergamo and Treasure Island.

He was made an Honored Artist of the RSFSR in 1978 and awarded the St. Petersburg theatrical prize Golden Soffit for the role of Dr. Dorn in the premiere performance Notebooks of Trigorin of Theatre Comedians (interpretation of Chekhov's play The Seagull).