An automatic storage and stacking device for sheets of laminar material, such as corrugated cardboard or the like, comprises a transportation unit which removes the sheets of laminar material from a cutting group, overlaps them and conveys them towards a storage surface. The transportation unit comprises a plurality of conveyors in series which can be operated at varying speeds so as to allow separation of a first series of sheets from a successive second series of sheets; with one of said conveyors there is associated a retainer for holding the rear portion of the first sheet of said second series, which retainer comprises a gripper member able to perform an alternating movement along the conveyor with which the gripper member is associated.