A method and machine for manufacturing foam parts are provided. The method generally includes cutting a plurality of sections across the width of the base sheet, engaging and reorienting at least one portion of each section, and joining the portions of each section in a desired configuration to thereby form a plurality of parts. The portions can be engaged by actuator assemblies operating in successively adjacent work spaces across the width of the base sheet to simultaneously produce a plurality of similar parts. In some cases, each part includes at least one portion that is reoriented relative to another portion, such as by rotating one of the portions or adjusting one of the portions to a position that is offset from the plane of the section.