The thermoforming press has a frame, a forming die assembly affixed to the frame, a mold-supporting table suspended to the frame under the forming die assembly, and a pair of molds mounted side by side on the mold-supporting table. A drive system is provided for imparting a pendulum movement to the mold-supporting table for alternately registering one of the molds with the forming die assembly while the other mold is positioned at a part retrieving station. The part retrieving and stacking mechanism has horizontal and angular displacements only as the vertical component of the retrieving motion is provided by the pendulum system. Spring discs are mounted between the forming die assembly and the press platen to control the forces generated between the forming die assembly and each mold.