A disposal system for stacking card-like objects neatly in a magazine. The cards enter the disposal system via a card entrance slot. A push plate located adjacent the slot pushes the cards past a pair of resilient snap elements in the sides of the magazine. A pressure plate is located behind the snap elements and biases the cards that have been pushed over the snap elements forward towards the rear of the snap elements. The cards are maintained in a stacked condition between the snap elements and the pressure plate. When a card is inserted into the card slot, the push plate is operated to an extended position, in which it pushes the card past the snap elements against the cards stacked between the snap elements and the pressure plate. The push plate then retracts, so as to enable another card to enter into the card slot. The user of the machine removes the magazine from the machine when the need arises or when the magazine is fully loaded with cards.