Composed in 1934, the Cello Concerto No.1 is not only the frist composition for cello by Milhaud, but also the most popular. It was dedicaated to Maurice Maréchal, who premiered it in Paris on June 28th 1935. This concerto was one of Grégor Piatigorsky's favorite concerti, as he kept it in his repertoire for several seasons after giving the U.S. premiere.

The first movement, Nonchalant, begins with a cadenza-like introduction for solo cello that contrasts with the music that follows. After the introduction, the orchestra plays the main theme quietly. The theme is later played for the cello against the background of a regular rhythmical accompaniment similar to a jazz texture.

The second movement, Grave, starts with bitonality in a low range and the solo cello playing a forceful yet passive aria-monologue.

The last movement, Joyeux, is brief and energetic. It starts in a march or fanfare style, and has a charming Latin American melodic and rhythmic flavor.