The Cello Concerto, written after the First World War, was influenced by the relative economy of means that the composer had discovered in his String Quartet and Piano Quintet of the preceding year. It differs from the Violin Concerto in particular in its intense concentration of material. He worked on the composition during the summer of 1918 with the collaboration of the cellist Felix Salmond, the cellist in earlier performances of Elgar's Quartet and Piano Quintet and later an influential teacher at the Juilliard School and the Curtis Institute. The first performance was grossly under-rehearsed, since the conductor of the rest of the programme, Albert Coates, described in her diary by Lady Elgar as "that brutal selfish ill-mannered bounder Coates", used rehearsal time allocated to the concerto for Scriabin's Poem of Ecstasy, keeping Elgar waiting for an hour. The public reception of the work was, in consequence, lukewarm, while some critics at least correctly apportioned the blame for the inadequate first performance of a major work by the greatest of living English composers.

The first movement opens with a grandiose statement by the soloist, leading, in almost improvisatory style, to a lilting melody announced by the violas. This is repeated by the soloist, who continues to dominate the movement. Plucked chords by the soloist lead to the second movement, a melancholy Scherzo, in which the soloist is again to the fore, with orchestration of the greatest economy. There is still greater poignancy in the brief slow movement, a continuous solo for the cello. The final Rondo opens with eight bars in which the first theme is suggested, to be interrupted by a declamatory statement from the soloist, before the movement is allowed to take its full course. Even then the excitement and joy of the principal theme are broken by references to earlier themes in the concerto and the mood of autumnal introspective melancholy that make this one of Elgar's greatest works. At the end of the score, where Haydn might have written Deo gratias, Elgar wrote the words Finis. R.I.P., intentionally or not signalling the concerto as the end of his creative life, the end of a war but also the end of an age.