Categorizing Shostakovich's Musical Style
Shostakovich had a notably diverse range of styles he composed in. His earliest works were neoclassical in nature, influenced heavily by Prokofiev and Stravinsky. Various piano pieces and his First Symphony fall under this category.

After breaking into the field of composition, he changed his focus to experimental modernism. This period is best represented by his satirical first opera The Nose and his Second Symphony. His opera Lady Macbeth of the Mtsensk District (1934). However, his music was denounced by the Soviet government in 1936, and thereafter took on a more conservative approach to his writing.

From 1936 onwards, his work was heavily influenced by Mahler's symphonies. Shostakovich thus reverted back to neoclassicism, but with a distinct flavour of romanticism. He is generally regarded as a neoclassical composer.

Other sources of influence include J. S. Bach's fugues, Beethoven's late quartets, Mussorgsky, and Alban Berg. Shostakovich also dabbled in a form of encoding messages into his music: for instance, his Tenth Symphony contains a motif whose notes spell out "E La Mi Re A" in dedication to a student of his with whom he was infatuated, Elmira Nazirova.

Neoclassicism
Musical neoclassicism was a movement developed in the twentieth century, and was particularly prominent between the two world wars. It was marked by a return to 18th-century styles, particularly from the classical period, although inspiration was also drawn from baroque literature.

Its emphasis on balance and emotional restraint is classical in nature; however, the incorporation of new harmonic techniques and the expanded instrumental range of the typical orchestra caused neoclassical music to sound distinctly twentieth-century in origin. Thus the term neo- (or, "new") classicism came about.

Prominent neoclassical composers include Prokofiev, Stravinsky, Bela Bartok and Paul Hindemith.

Examples of His Music
Click the following link to listen to an example of Shostakovich's music.

Chamber Symphony for Strings: mvmt. 2, Allegro molto [2:57]