When a pressure safety valve actuates, thrust forces are developed. These thrust forces must be considered for the proper installation of the relieving device. For gas or vapor compressible flow, Simpson developed thrust force plots that can be used to calculate the magnitude of the thrust force, Although these charts are available in the open literature, the assumptions behind the charts and the underlying equations are not. This article addresses these issues. All equations and fundamental assumptions are stated and all flow models are explained. Numerical examples are given to illustrate the use of the equations and the corresponding Simpson Charts. In addition, several important modifications to the original charts are noted. The thrust force equations for a relief valve operating with a subcritical nozzle and a subcritical outlet, which are absent from the original Simpson Charts, are included here. The extent of the region where the relief valve operates with a critical flow nozzle and a subcritical flow outlet is modified to account for backpressure effects. Finally, the concept of a minimum relief valve outlet to nozzle area ratio is introduced. (c) 2006 American Institute of Chemical Engineers