Apparatus for automatically laying up veneer sheets for the manufacture of continuous veneer panels composed of a plurality of stacked sheets, optionally glued on their top face. The apparatus includes a frame, a conveyor for receiving the veneer sheets transversely and for successively feeding said veneer sheets in a timed manner into the apparatus, the conveyor having an alignment device for aligning the sheets and having lug members for pushing against the back transverse edge of each of said sheets, thereby urging said sheets forward. The conveyor running on a track having a upward trajectory portion and an inverted trajectory portion so that the sheets are gradually flipped top face down. The sheets are maintained against the conveyor by vacuum hoods mounted behind and between the conveyor. When reaching their inverted position, the sheets transfer onto a suction box having suction feet substantially straddling the inverted portion of the conveyor. The suction box is connected to a vacuum source and is movable up and down by an controllable stroke for sequentially depositing veneer sheets, stacking them in a predetermined order on a discharge conveyor.