Within the last two decades, the use of elastic finite element analyses to demonstrate design compliance with the rules of the ASME Code has become a generally accepted engineering practice. Linearized stresses from these analyses are commonly used to evaluate primary stresses. For redundant structures or complex structural details, the use of such analyses, instead of simple equilibrium models, often results in significant overconservatism. Direct use of finite element results is often preferred because equilibrium solutions are not unique and effective equilibrium models are not easily constructed for complex three-dimensional structures. However, finite element analyses include secondary stresses, even for pressure, mechanical, and shock loading. For primary stress evaluation, the ASME Code allows the use of inelastic methods based on lower-bound solutions and plastic analysis. For primary stresses, the Code requires equilibrium to be satisfied without violating the yield strength of the material. The use of finite element inelastic analysis to partition mechanically induced stresses into the primary and secondary categories was introduced by Porowski et al. (1993). The latter provides a detailed discussion of the technical approach and the results for the axisymmetric junction between the plate and shell in a pressure vessel. This example was selected by the Session Organizer as a benchmark case to compare the efficiency of various analytical approaches presented at the Session. The authors have since used this approach to design more efficient structures. The practical application of this method to reduce the weight of complex redundant structures designed to meet primary stress limits is described herein for a more complex three-dimensional case. Plastic design utilizes the ability of actual materials to find the most efficient load distribution. A heat exchanger subjected to pressure, accelerations, and nozzle external loads is evaluated as a practical example. The results of elastic analyses are compared with those obtained by inelastic analyses. It is shown that inelastic analyses can be used effectively to reduce the weight of structures using only modern PCs for the engineering computations, as illustrated in this paper.