The power semiconductor module (1) has a plastics housing (2) with internal struts (7), fitted with a metal or metal/ceramic multi-layer substrate (11) in its base plane. The inwards facing surface of the substrate is provided with the semiconductor components (12) and associated terminals (3), the interior of the housing filled with a soft resin mass (10) overlaid by a hard resin mass (9). The internal struts extend as far as the soft resin mass without direct contact with the substrate, their free ends widened to provide anchoring points, the soft resin mass pref. having a Shore hardness of greater than 20.