The paper attempts a revisionary analysis of Tennessee Williams’ A Streetcar Named Desire by focusing on the positive aspect of desire in light of Gilles Deleuze and Felix Guattari’s postmodern philosophy of affect and becoming. While the critical interpretation of the play has tended to revolve around Blanche and Stanley’s conflict in terms of binary oppositions, their similarities―sexual and alcoholic indulgence, for instance―and the complexity of their characters challenge such a schematic reading. Inconsistent and often similar to each other, the characters of Streetcar are non-hierarchical and anti-essentialist entities―what Deleuze and Guattari call ‘desiring machines’―whose differences are only a matter of degree or intensity. Driven by desire, they affect and are affected by each other while making new connections and reconstituting old ones as they become something else. Rather than dramatizing a clash between different individual beings and the destructive consequences of desire, Streetcar is a play of becoming that attests to the productive and revolutionary potential of desire. Blanche’s relations with the other characters ultimately lead to the deterritorialization of the French Quarter and destabilize old ties that kept them dependent on or even subject to others. In this respect, the play celebrates body’s infinite potential to affect and be affected and produce real consequence as a play of anti-fascism. The play’s politics of becoming, evinced by Williams’ nuanced portrayal of the characters, challenges us to imagine new possibilities of identity and relationship in postmodernity.