A slicing machine comprises a frame having a support surface (10) onto which the block of material to be sliced is placed, a cutter assembly (14) for moving in a cutting plane transversely of said support surface, said cutter assembly being movable between upper and lower positions (K, K1) and a pusher (11) for moving the block of material in stepwise fashion towards said cutting plane, said pusher being movable from a rearmost position (A) in a forward direction during successive slicing operations to a forwardmost position (A1) close to the cutting plane. A pivoted retainer (22) is pivotally connected to the frame and movable between a non-retaining position and a retaining position for retaining and supporting the last slide of the block. The retainer is actuated by a pneumatic rotary actuator. The pusher moves toward its rearmost position as soon as the last slice is in a retained and supported situation. Preferably the retainer comprises a substantially U-sectioned elongate member (21) having a base and sides pivotally mounted at its sides on a fixed part of said machine, said member being movable between a raised inoperative position where it remains during each slicing operation and a lower operative position.