An injection device includes: a housing with a product container in which a stopper with a bearing face can be moved to a stopper end position and which, proximally to the stopper end position, has a minimum product container cross section; a drive configured to move the stopper, which includes a plunger rod with a drive face that contacts the bearing face; a plunger rod guide is arranged outside the product container and guides the plunger rod, with a plunger rod guide cross section adapted to a plunger rod cross section. The product container only incompletely guides movement of the plunger rod and the plunger rod cross section is not prevented from moving in a tilting direction by the minimum product container cross section, and a plunger rod centering aid a distal end of the plunger rod limits the movement of the plunger rod in the tilting direction.