This paper proposes engineering estimation equations of elastic-plastic J and COD fur axial through-wall cracked pipes under internal pressure. Based on detailed 3-D FE results based on deformation plasticity, the plastic influence functions for fully plastic J and COD solutions are tabulated as a function of the mean radius-to-thickness ratio, the normalized crack length. and the strain hardening. Based on these results, the GE/EPRI-type J and COD estimation equations are proposed and validated against the 3-D FE results based on deformation plasticity. For more general application to general stress-strain laws or to complex loading, the developed GE/EPRI-type solutions are re-formulated based on the reference stress concept. Such a reformulation provides simpler equations for J and COD, which are then further extended to combined internal pressure and bending. The proposed reference stress based J and COD estimation equations are compared with elastic-plastic 3-D FE results using actual stress-strain data for Type 316 stainless steels. The FE results for both internal pressure cases and combined internal pressure and bending cases compare very well with the proposed J and COD estimations.