A deep-drawn paper tray made of paper material, a method and an apparatus for manufacturing the tray, and a closed product package comprising the tray. The tray having a bottom and upwardly expanding side walls around the bottom, the side walls of the tray being shaped to expand through a plurality of circumferential steps dimensioned low enough for obtaining wrinkle-free side walls for the tray. The outermost step is a flat, wrinkle-free rim flange, which enables liquid and gas proof heat-sealing of a lid to form the package. The apparatus may comprise upper and lower moulding tools with concentric movable frames for forming the tray bottom and side wall steps from paper blanks, and moulding tools may be mounted onto a rotating turret carrying a paper blank through working stations arranged along the turret circumference, to shape the tray bottom and the side wall steps at the consecutive stations.