A stacking system for aligning and stacking stamped sheet metal parts is provided. The stacking system includes a frame configured to coordinate a plurality of sub-systems including a parts catcher, receiving head including a plurality of alignment cylinders, and a set of elevating tables on a shuttle platform. Parts are received by the catcher from a conveyor belt and transported to a receiving head for alignment to a targeted position. After the formed part is aligned to the stack, the lift table is lowered such that space is available for another part to be aligned. After a predetermined number of formed parts has been stacked, a table shuttle will slide the lift table to an unloading position accessible by a fork truck.