The Pressure Vessel Research Council (PVRC) of WRC initiated a group sponsored program aimed at improving residual stress estimates for a broad range of realistic weld geometries and procedures. The objective was to improve tools for fracture mechanics based fitness-for-service assessments@ rationalize postweld heat treatment (PWHT) times and temperatures and improve procedures for local PWHT. Of particular interest are pressure vessel and piping components including pipe girth welds@ seam welds@ and nozzle-to-head attachment welds and the like. Before embarking on the finite element studies covered by the scope of work for PVRC's program@ a critical assessment of the state-of-the-art was made by the Bulletin's authors. It was observed that large discrepancies in residual stress estimates occur among various investigators due to differences in models@ computational procedures and materials properties used. The implications regarding integrity assessments and recommended welding @ repair and heat treatment procedures are profound and have significant financial importance. The validation and basis of the methods to be used in PVRC's program are described herein. A specific objective of the program is to be able to apply in a novel manner parametrically expressed residual stress distributions developed with consideration of welding procedures and joint restraint. The residual stress modeling techniques offered by the Bulletin's authors here have also been independently validated for many nuclear@ heavy fabrication@ and aerospace applications. This report@ authorized for release by the project sponsors@ includes not only a valuable bibliography but also a close look at the problems associated with obtaining reliable answers about residual stressses. It is important that those seeking to incorporate estimates of residual stresses in practical engineering and research activities be aware of the shortcomings of much of what is reported in the literature and elsewhere. Assumptions made regarding heat flow@ hardening behavior and materials properties among others can invalidate results. It is expected that this report of PVRC's study will lead to acceptance of the results of PVRC's project and higher standards for the performance of research