This paper presents the development of variable geometry dies that enable the extrusion of plastic parts with a varying cross section. Extrusion accounts for 40% of all manufactured plastic parts because it is a relatively low-cost and high-production-rate process. Conventional polymer extrusion technology, however, is limited to fixed dies that produce continuous plastic products of constant cross section defined by the die exit profile. A shape-changing die allows the cross section of the extruded part to change over its length, thereby introducing the capacity to manufacture plastic faster and with lower tooling costs than injection molding. This paper discusses design guidelines that were developed for movable die features including revolute and prismatic joint details, land length, and the management of die leakage. To assess these guidelines, multiple dies have been designed and constructed to include an arbitrary four-sided exit profile where changes were made to the internal angles and length of sides as the extruder was operating. Experimental studies were conducted by using different extruder line settings and time between die movements. Test results are presented that include shape repeatability and the relationship between extrudate profile and die exit geometry.