This paper provides plastic limit load solutions of cylinders with circumferential part-through surface cracks under combined axial tension, internal pressure and global bending. Such solutions are developed based on detailed three-dimensional (3-D) finite element (FE) limit analyses using elastic-perfectly-plastic material behaviour, together with analytical solutions based on equilibrium stress fields. For the crack location, both external and internal cracks are considered. Furthermore, in terms of the crack shape, both semi-elliptical and constant-depth surface cracks are considered. The resulting limit load solutions are given in a closed form, and thus can be easily used in practical situations. Being based on detailed 3-D FE limit analysis, the present solutions are believed to most reliable, and thus to be valuable information for integrity assessment of piping.