Shafran pursued a career as soloist and recorded very widely. His repertoire included the major concertos, music for cello and piano, and the solo cello repertoire. His astonishing technique in the higher register enabled him to perform a wide range of violin works at original pitch. He also sought to enrich the cello repertoire, and made and performed transcriptions of works for other instruments. However, he rarely toured outside the Soviet Union and the Eastern bloc, and virtually all his recordings were for the Melodiya label, so his international reputation was very limited.