The concerto is scored for solo cello, one piccolo, one flute, two oboes, two clarinets (each doubling B-flat 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 concerto lasts around 35 minutes and has three movements:
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 signaled the beginning of Shostakovich's late period style.
Like the Fourth Symphony and Ninth String Quartet before it and the Fifteenth Symphony after it, the Second Cello Concerto gave Shostakovich some problems in the compositional stages. The opening Largo, for example, was originally conceived to be the start of a new symphony. Shostakovich later abandoned this idea, however, and reworked this movement into its present form. The finale also gave the composer considerable trouble. He confessed to Mstislav Rostropovich, the concerto's dedicatee, that he had a finale completely written out but decided to scrap that version and supplant it with the one we know today because he felt that his original finale was weak. Shostakovich also allowed Rostropovich to make a few changes to the concerto's cadenzas.
Concerto for Cello and Orchestra No. 2 in C Major, Op. 126, was written in 1966. In point of time this concerto appeared after Dmitry Shostakovich had re-orchestrated Schumann's Cello Concerto in 1963, including it in the list of his works as Op. 125. Shortly upon composing his Second Cello Concerto Dmitry Shostakovich performed the same service to his pupil Boris Tishchenko in re-orchestrating the latter's First Cello Concerto. Shostakovich began work on his Second Cello Concerto in Moscow presumably in the spring of 1966 and completed it at the Oreanda health resort, Yalta, on April 27 (that is the date on the last page of the autograph score). Shostakovich's Second Cello Concerto was first performed at the concert marking his 60th birthday, held in the Large Hall of the Moscow Conservatoire on September 25, 1966. Duration: approx. 36'. The composer's reduction for cello and piano was published by the Soviet Composer in 1969. The whereabouts of the autograph is not known. The present publication, based on the edition which appeared in the Music, Moscow, 1976, has been collated with the autograph full score, its 1970 edition and the piano score published in 1969.