Stefan Wolpe wrote the Trio for Flute, Cello, and Piano during a period of newfound professional recognition in America. In the 1960s, a young generation of American composers and musicians came to appreciate the émigré composer as a carrier of the radical traditions of the Bauhaus and Second Viennese School. The Trio for Flute, Cello, and Piano was commissioned by the Group for Contemporary Music, and completed while the composer was on a Guggenheim Fellowship in Rome. During this time, Wolpe began to refine what would come to be known as his late style: he sought to simplify his aesthetic, to reduce the external complexity of his works in order to clarify their inner processes.

It is important to note, however, that Wolpe's "processes" were quite different from those of other composers. Though he worked with adapted serial methods, he sought to reach beyond serial operations that organize numerically and find means for incorporating expressive associations into his compositional theory. In order to do this, he created "processes" that involved groups of notes that were assigned "specific organic tasks or organic habits." In other words, a specific set of notes would assume a particular shape, texture, and mode of behavior. As he described in a letter, it was these kinds of processes that he sought to clarify: "I am working on the Trio for Wuorinen and writing an amazing (that is I am amazed) piece of simple events in a less simple syntactical environment ... I wonder about the unweight of leaves, and letters, and facial expressions ... to the pitch configuration itself belongs characteristic morphological structures (conditions, behavior forms, cast-like proportions, reduced dynamics, etc.)."

The Trio for Flute, Cello, and Piano is significant within Wolpe's catalogue because it fuses this innovative, highly personalized approach with traditional formal ideas. The structure of the trio's first movement, for instance, resembles sonata form. This might seem surprising, given Wolpe's antagonism toward traditionalism and his zeal for relentless progress and renewal. Yet, Wolpe also claimed that "one's attitude must remain ever alerted by examining rigorously and without fear how much history one carries along with oneself, and whether this load, in effect, interferes with a radical attack on all genuinely fresh musical problems." Historical reflection seems to have assumed an increasing prominence in the aesthetic of Wolpe's later works. This music, however, remains as provocative and ruthlessly innovative as ever.

The first movement of the trio fuses sonata form with classic twelve-tone techniques and Wolpe's own "organically" motivated harmonies and gestures. It begins with an exposition—an evanescent web of clearly defined, rhythmically charged gestures, shapes, and images. Throughout this piece, these are expressed as Klangfarbenmelodien—literally "sound color melodies"—or single melodies carried by multiple, successive instruments. An extended development section ensues, which consists of several starkly contrasting sub-sections. In some of these, modified fragments of the original gestures interrupt and overlap with one another. Calm, translucent sub-sections mediate between dense ones. A short recapitulation then introduces modified versions of the opening gestures. It leads to a frenzied climax, a short cadenza-like flute solo, and an extended coda. The second movement, which does not adhere to sonata form or any other traditional scheme, embodies the same radical and eclectic aesthetic.

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