Knaifel was introduced to his profession by his musician parents, both of whom taught at the Leningrad Conservatory. Strict training began at age seven with cello lessons at the Rimsky-Korsakov College of Music (an affiliate of the Leningrad Conservatory), and then in 1960 he entered the class of the legendary Rostropovich at the Moscow Conservatory. But a career as a cellist was not in his cards -- injury-plagued and frustrated, Knaifel abandoned his cello studies to pursue a course in composition back at the Leningrad Conservatory (1963 - 1967). He has since then worked and lived in that city (now St. Petersburg).
Knaifel is something of a musical metaphysicist, one inclined towards both undefined abstraction and deep spiritual-religious sentiment. (He is a confirmed member of the Russian Orthodox Church.) He reduces music to its most basic building blocks: sound as sound, and for the sake of sound. But basic does not mean short, and Knaifel has written many pieces that last several hours (only one of which, The Canterville Ghost of 1966, is an opera and might thus be expected to be of great size). He does not apply traditional, generic titles (like "symphony" or "quartet") to his pieces, preferring instead either pseudo-descriptive ones, like Bezumie (Madness, 1987), or liturgical ones, like Agnus Dei (also 1987), and he has divided his energy almost equally between instruments and the human voice.