A connection of a bearing bolt (6) in a cylindrical housing (1) of a roller tappet (2) that is actuated in a direction of a longitudinal axis (Z) is provided, especially for a tappet push-rod valve drive of an internal combustion engine. The bearing bolt (6) is supported in bore holes (7) of the housing (1), which extend in a transverse plane (XY) to the roller tappet (2), perpendicular to the longitudinal axis (Z), and is connected with a positive and/or non-positive fit to the housing (1) through material deformation. The material deformation is provided as one or more segments (9, 10), of which at least one segment (9) completely encloses a radial load zone (16) of the bearing bolt (6), and a section (15) of the bearing bolt (6) extending about the transverse plane (XY) is free from material deformation.