The mechanical stress caused by flux pinning in a cylindrical superconductor with a concentric hole is investigated theoretically. Exact expressions for the radial and hoop stress are derived using the critical-state model. Stress profiles during a magnetization process often used to activate high-T c superconductors as strong trapped-field magnets are presented and analyzed in detail. It is shown that due to the hole the tensile hoop stress is enhanced by a factor of 2 or more, depending on the hole diameter. The dramatic increase in cracking probability is emphasized.