As noted in its preface, The American Dream is an allegory of the "American Scene" gone awry, a Scene typified here by a sadistic Mommy, emasculated Daddy, and embittered Grandma. The play imagines what is left of the American Dream in their shared household.
The American Dream is personified by the Young Man, a clean-cut, Midwestern beauty, a self-described "type". Though physically perfect, he remains incomplete, having lost all feeling and desire in the murder of an identical twin from which he was separated as a child. This twin—Mommy and Daddy's first adopted son—stands against his brother as a consummate deformity. He lacks a head, spine, guts, feet of flesh, and onward. Moreover, he suffers a progressive disfigurement under Mommy's sadistic tortures, punishments specifically directed at each of his bodily excesses and infantile desires. Thus: an eye for only having eyes for Daddy, his "you-know-what" for masturbation, and onward.
In his unruliness, this child—the so-called "bumble of joy"—fails to provide Mommy and Daddy what the demand above all: "satisfaction". The result of these tortures is the Young Man, a man disemboweled, voided of interiority but perfect in form, a figure who cannot relate to others but accepts the "syntax" around him in knowing that others must relate to him. Thus he becomes the son who provides Mommy and Daddy the satisfaction they believe that they have long desired. Doing anything for money, he is in some sense their perfect commodity, the merchandise they wanted all along.
Albee's allegory of the American Dream is certainly strange. The American Dream does not appear as that which one lives out or even as ideology, but as a person and possession. One possible reading of this allegory involves the all-important theatrical concept of the mask. Linked indissolubly, the twins are in some sense figures for the actor and his mask. The Young Man as American Dream is a mask without a man behind it, a personification without a person. As he tells Grandma, he is a type. The murder of his double is the murder of the man behind the mask, the elimination of the unruly body—indeed, the "bumble"—that can only mould itself into the perfect form through its mutilation. The product of this mutilation is the Young Man. Thus Albee offers a sinister account of the American Dream, imagining it as a mask disemboweled of man and his excesses.
As the above discussion of the mask might suggest, The American Dream concerns itself intimately with the relationship between language and violence. This exploration involves both language's violent uses in social intercourse as well as violence performed on language itself—violence that more precisely describes many of what critics celebrate as the play's most "absurdist" moments. As for the former, Grandma certainly underlines the violence in social intercourse staged against old people; emasculation is another primary example of this violence as well. Language's capacity for violent effects often lies in its "performative" qualities. The concept of the "performative"—that is, language that does something—is crucial to the play.
One of the primary violence's the play stages is Mommy's assault on Daddy. As with many of Albee's female characters—Martha from Who's Afraid of Virginia Woolf perhaps being the most memorable—Mommy is the consummate "bad mother": sadistic, jealous, greedy, and onward. At some level, the play leaves the spectator enthralled with Mommy's sadism: the effect it generates is one of a masochistic submission to her violence. The victim of her violence above all is Daddy, whom she infantilizes at every turn. Thus, for example, she forces him to echo her story of the beige hat. She derides with her exaggerated encouragement when he moves to open the door, pathetically attempting to demonstrate his masculinity. As noted above, she mutilates the "bumble of joy" for his bodily excesses and infantile desires: the Young Man, a negative entity of sorts, is the result.