How do "The Cask of Amontillado" and "Young Goodman Brown" relate to Formalist critical theory?

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Russian Formalism was conceived as an objective, scientific approach to examining literary texts to determine the systematic structural and technical aspects, or "functions," that determined its "literariness" while, at the same time, Formalism used these examinations to define literariness and explain how literary representation of reality differed from objective reality. Formalism undertakes to examine key aspects of a literary work (focusing originally on poetry) by analyzing it for literary device functions and structural aspects.

Literary device "functions," some few examples of which are:

Structural concepts, the most significant of which are:

  • literariness
  • form (form => content)
  • foregrounding
  • defamiliarization
  • estrangement of the reader
  • expert reader
  • literary language
  • automatization of experience
  • plot/fabula
  • story/sjuzhet
  • deep meaning (sjuzhet, story)
  • surface meaning (fabula, plot)
  • universalities
  • chronological sequence
  • manner of emplotment
  • dichotomies
  • narratology

What you are asking, then, is how these functions and structural concepts can or cannot be applied successfully to these two stories. As you can see from these lists of particulars, these may all be successfully applied to any work of literature. Let's take a look at these two works for illustration.

In "Young Goodman Brown," symbolism is evident from the very first lines: "Faith, as the wife was aptly named." The deep meaning contained in the fabula (story) is an ancient one: a seemingly good person sells their soul to the devil. The surface meaning emplotted in the sjuzhet (plot) is that a faithful Christian man, married to a seemingly faithful Christian wife living in a faithful Christian community, is tragically surprised to discover that none are faithful, all except him have sold their souls to the devil and he is thus surrounded by the loneliness of resistance to wrong-doing.

In "The Cask of Amontillado," the story is chronologically framed as a flashback reminiscence in which Montresor tells some anonymous someone of a past deed of horror. In the sjuzhet (plot), readers are estranged from a culturally familiar fraternity (though secret), "You are not of the masons. ... Impossible! A mason?" while it is defamiliarized through foregrounding when, a sign being demanded, Montresor shows a mason's brick-laying trowel:

"A sign," he said, "a sign."

   "It is this," I answered, producing from beneath the folds of my ROQUELAIRE a trowel.

   "You jest," he exclaimed, recoiling...

Both stories can be analyzed through a successful application of Formalist critical theory. Both structure and function (devices) can be identified and examined in each story and both deep and surface meanings can be uncovered, while universalities in their literariness (that which is common to all literature as opposed to that which is unique to one work) can be ascertained.

Note that Russian Formalism became Czech Formalism, which spread to America as American Formalism, which then became American New Criticism. So while Formalism and New Criticism are related, they are vastly different in approach, e.g., while Formalism wholly disregards author, society and culture, New Criticism begins analysis with author and historical context.

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