A power semiconductor module is provided, having a substrate. A housing and a switch device surrounded by the housing are arranged on the substrate, wherein the switch device has a base and a connecting device, and the connecting device has first and second main regions. A power semiconductor component is disposed on a conductor trace of the base and is provided with a pressure device formed to bemovable in a normal direction of the base. The pressure device has a pressure body and a pressure introduction body, wherein a pressure element protrudes from the pressure body and is pressed on a part of the second main region of the connecting device, with the part being arranged in a projection zone of the power semiconductor component along the normal direction of the base. The pressure introduction body is supported on the substrate by means of at least two fastening devices bonded in opposite bearings of the substrate, wherein the geometric center points of the opposite bearings and thebase are on a straight line.