A power semiconductor module that includes a substrate having at least one power semiconductor element; a heat sink for dissipation of heat from the at least one power semiconductor element and a housing having a cutout which is arranged on a lower face of the housing facing the heat sink and holds the substrate; and to a method for production of such power semiconductor modules. The power semiconductor module has at least one holding element, which engages in a recess, which is associated with the at least one holding element, on the lower face of the housing and is designed such that it limits any movement of the substrate in the direction of the lower face of the housing.