In the 1960s, Beasley's first work consisted of welded sculptures made from broken cast iron. This work brought him national recognition when in 1961 one of his sculptures was included in the ground breaking exhibition The Art of Assemblage at the New York, Museum of Modern Art a piece which appeared in an exhibition which Philip Linhares, Chief Curator of Art of the Oakland Museum of California referred to as "seminal". The following year his assemblage sculpture "Chorus" was acquired by New York's Museum of Modern Art, making Beasley the youngest artist to have work in the permanent collection. In 1961, while a student at Berkeley, Beasley joined Peter Voulkos in building one of the first sculptor-built foundries, the storied Garbanzo Works that was instrumental in the Renaissance of bronze casting in American sculpture. Following an abstract esthetic, he began casting sculptures in bronze and aluminum. In 1963, he was one of eleven artists to represent the United States at the Biennale de Paris, where French Minister of CultureAndre Malraux awarded him the purchase prize. In 1968, Beasley began investigating the use of transparency as a sculptural medium. He was successful in creating small transparent sculptures in cast acrylic but experts at Dupont and Rohm & Hass were convinced that it was impossible to do castings as large as Beasley envisioned. That year, the State of California invited Beasley to participate in a competition for a monumental sculpture for the state. At first, the jury was unaware that Beasley was experimenting with transparency as a sculptural medium and invited him based on his work in cast metal. Beasley was determined to pursue transparency and proposed a monumental cast acrylic sculpture. Upon seeing Beasley's proposal, they questioned the sculptor about its viability. He convinced them that creating what he envisioned was no problem but privately knew that he would have to invent a new process, which he did. His proposal for Apolymon, a transparent sculpture in cast acrylic won and he installed the piece in Sacramento in 1970.
1970s
Fascinated by the esthetics of transparency, Beasley worked in cast acrylic for the next ten years. In 1974, members of the undersea research community approached Beasley to see if he could adapt his technique to cast transparent bathyspheres for undersea exploration. He succeeded in creating the bathyspheres for Johnson Sea Link submersibles for Harbor Branch Oceanographic Institute. It was these submersibles that were deployed to locate the crew compartment on the bottom of the ocean after the Space Shuttle Challenger disintegrated upon liftoff in 1986. Beasley continued to make transparent sculpture for the next ten years. His transparent sculptures were exhibited widely both in the US and abroad including solo exhibitions in 1972 at the DeYoung Museum in San Francisco, the Santa Barbara Museum of Art, the San Diego Museum of Art, and group shows including the Salon de Mai in Paris and at Expo 70 in Osaka, Japan.