A power semiconductor module arrangement includes a substrate arranged in a housing. The substrate includes a first metallization layer arranged on a first side of a dielectric insulation layer and a second metallization layer arranged on a second side of the dielectric insulation layer. At least one semiconductor body is mounted on a first surface of the first metallization layer facing away from the dielectric insulation layer. A connecting element is arranged on and electrically connected to the first surface. A contact element is inserted into and electrically connected to the connecting element, and extends from the connecting element through an interior of the housing and through an opening in the cover of the housing to an outside of the housing in a direction perpendicular to the first surface. A hard encapsulation is arranged adjacent to the first metallization layer and at least partly fills the inside of the housing.