A machine for producing cardboard plates or the like comprises punching apparatus for punching or cutting off pieces of sheet material and delivering them edgewise under gravity to be received alternately by two containers. One container is open at each end, the second is permanently closed at one end. The first container is fixed to an oscillating unit and the second is pivoted thereto. When swinging in one direction the unit carries the first container to a position for receiving a piece from the punching apparatus and the second container to a vertical guiding element leading to one pair of dies on a twin press. In the reverse movement, the oscillating unit carries the first container to a position for feeding its piece through its opposite end to a second vertical guiding element leading to the second pair of dies in the press. In this movement, a link swings the second container about its axis on the oscillating unit to present the open end of the container to the punching apparatus. Controlled flaps prevent the pieces from falling prematurely from the containers. The pairs of dies are actuated alternately by a curved rotary thrust element.