How is modernism reflected in Animal Farm?

Through various artistic media, modernism sought to construct an alternative reality to the one undermined by the cataclysm of the First World War. Western culture was in a state of crisis, with the old certainties—moral, intellectual, and social—now being seriously challenged for the first time. This period of unrest gave rise to a variety of different political movements, such as Soviet Communism, which is the object of Orwell's satire in Animal Farm.
Traditional society, in the person of Mr. Jones the farmer, has failed, and the animals take this opportunity to destroy the old world completely and usher in a brave new utopia in which animals will finally be liberated. It is in the fractured aftermath of such radical upheaval—be it the First World War or the Bolshevik coup of October 1917—that modernism finds its materials, and which it then uses to explore the subjective responses of individuals caught up in the middle of social chaos. One sees this in how the different animals on the farm react to the new order of things, each one effectively having to forge new identities in the heat of rapidly shifting political realities.
Orwell's literary style in Animal Farm may not be modernist, but the events that take place in the story perfectly encapsulate the kind of social malaise that provided a catalyst for this most fascinating and complex of artistic movements.

Modernist literature, especially after World War I, showed disillusion with the state of civilization, a questioning of the notion of progress, an interest in language, and experimentation with literary form. Animal Farm does not exactly fit the ideal of a modernist novel, as it is written using traditional forms—fable, fairytale, allegory—but it does fit the first two characteristics, at least to some extent.
Orwell's fable is a critique of the modern world, especially of Soviet totalitarianism under Josef Stalin. Animal Farm shows no hope in progress but is, instead, a bleak tale of disillusion in which the early dreams that the rebellion would bring equality and plenty to all are crushed.
Animal Farm also focuses on language. Classic modernism is more concerned with experimenting with language than is Orwell, but he, like the modernists, is acutely concerned with the importance of paying attention to words and meaning—just like the modernists he doesn't want his audience to be lulled into complacency about language. He shows that much of the animal's downfall and subordination to the pigs comes because they are not vigilant or attentive enough to how language is used and abused.
All this being said, Animal Farm has modernist elements, but is not experimental enough to be a classic modernist piece in the vein of Virginia Woolf, Gertrude Stein, or James Joyce.

George Orwell's novella Animal Farm is a prime example of modernism. This genre grew and was popular between 1910 and 1960. During this time period, the world experienced the horrors of several wars. The genre is typically characterized by a declining civilization and the questioning of humanity's survival. Often, modernist writers use irony and satire to show the isolation of a character or characters from the rest of society to point out the problems within that society.
Orwell's work is an allegorical political satire that shows readers the terrors of what happened when communist leaders Joseph Stalin and Leon Trotsky (represented by the characters of Napoleon and Snowball) rose to power in Russia in 1922.
Throughout the story, readers see an out-of-control government and wonder how the characters will survive such a flawed society. Like any other modernist story, Animal Farm does not have a happily tied-up ending.