Three-dimensional (3D) constraint effects for part-through cracks, such as corner and surface cracks, emanating from stress concentrators play important role in damage tolerance design of structures, but have hardly been investigated in the frame of 3D elastic–plastic fracture theory. Here the ability of current elastic–plastic solutions to describe 3D constraints and their effects on crack tip fields of corner and surface cracks emanating from stress concentrators are systematically analyzed using finite element (FE) method. Distribution of the out-of-plane constraint factor Tz and corresponding in-plane constraint parameters QT and AT can quantify the effect of stress concentration on crack tip fields. Good agreement between 3D elastic–plastic solutions (J-Tz, J-Tz-QT, J-Tz-AT) and FE results is obtained for four typical specimens at relatively high and low loading levels, showing that these solutions can serve as the theory foundation for advanced damage tolerant analyses of engineering structures.