In many structural members, out-of plane stress due to bending and in-plane stress due to extension act at the same time. In the present paper, the characteristics for fatigue crack propagation and brittle fracture initiation from a through thickness crack in a plate under arbitrary combined extension and bending are analysed theoretically using ρ⁺-concept. Considering the stress balance within the plate thickness, the authors defined effective tensile plastic zone size (ρ⁺_eff) or effective stress intensity factor ( K _eff) as a criterion of brittle fracture initiation and fatigue crack propagation. The effectiveness of this criterion were confirmed by brittle fracture initiation tests and fatigue crack propagation tests.