For the design of a transmission piping system, a stress intensification factor (SIF) is generally used for the stress calculations of piping components due to external forces, and the solutions for the single-walled piping components can be found in the existing design codes. However, it is quite difficult to obtain the reliable estimations for pipe-in-pipes (PIPs) from the existing solutions, because the PIPs show significantly different behaviors compared to the single-walled piping components due to the restraint effect induced by the outer pipe of the PIP. In this paper, the estimation schemes for the stress behaviors of the PIPs were proposed based on the detailed finite element (FE) analyses. In order to quantify the restraint effect, the FE analyses were conducted by considering various geometric variables of the PIPs under an internal pressure and a global bending moment. Based on the FE results, the tabular and closed-form solutions of the SIFs of PIPs were newly proposed. Finally, the proposed SIF estimations were validated against numerical results.