Like the first concerto, it was written for Mstislav Rostropovich, who gave the premiere in Moscow under Yevgeny Svetlanov on 25 September 1966 at the composer's 60th birthday concert.
Along with the Eleventh String Quartet, the Preface to the Complete Works, and the Seven Romances on Texts by Alexander Blok, the Second Cello Concerto signals the beginning of Shostakovich's late style.
He confessed to Rostropovich that he had a finale completely written out but decided it was weak, scrapped it, and replaced it with the one we know today.
The concerto is scored for solo cello, one piccolo, one flute, two oboes, two clarinets (each doubling B♭ and A), two bassoons, contrabassoon (doubling 3rd bassoon), two horns, timpani, slapstick, wood block, tom-tom, tambourine, snare drum, bass drum, xylophone, two harps (always in unison as indicated on the score), and strings.
The exchanges continue until the cello leads the orchestra into a climax, which gives way to a cadenza restating the opening material, punctuated by bass drum thumps.