A method and an automatic layup system for making a stack of a plurality of composite plies are presented. The automatic layup system includes a stacking assembly located in a first plane and a layup tool located in a second plane parallel to the first plane. The stacking assembly and the layup tool are movable towards each other. The method includes the steps of (a) providing one or more composite sheets between the layup tool and the stacking assembly, (b) generating a first composite ply from the one or more composite sheets, (c) placing the first composite ply on the layup tool by the stacking assembly by bringing the stacking assembly and the layup tool close to each other, and (d) repeating the steps (b) and (c) for generating and placing a second composite ply on the first composite ply, which is placed on the layup tool.