In the present paper, the closed-form expressions for the stress intensity factors (SIFs) and the elastic crack opening displacements (CODs) of complex-cracked pipes are derived based on the systematic three-dimensional (3D) elastic finite-element (FE) analyses. The loading conditions that are evaluated include global bending moment, axial tension, and internal pressure. In terms of geometries, the geometric variables affecting the SIFs and the elastic CODs of complex-cracked pipes, i.e., the crack angle of through-wall cracks (TWCs), the crack depth of fully circumferential, internal surface cracks in the inner surface of pipe, and the ratio of pipe mean radius to thickness, are systematically considered in the present FE analyses. The FE analysis procedure employed in the present study has been validated against the existing solutions for the circumferential TWC pipes. Using the present FE results, the shape factors of SIF and elastic COD for complex-cracked pipes are tabulated as a function of geometric variables. The results are applied for closed-form expressions of SIF and elastic COD when the pipe is subjected to simple loading conditions of bending, axial tension, or internal pressure. The proposed closed-form expressions can estimate SIF and elastic COD of complex-cracked pipes within maximum differences of 2.4% and 5.9% with FE results, respectively.