This paper describes the application of the boundary point least squares approach to the plane stress analysis of tube sheets with either mechanical or thermal loads. The paper includes a derivation of appropriate stress functions, a discussion of the point matching and boundary point least squares methods, and a description of the application of the method to the analysis of different hole configurations in tube sheets. It concludes with numerical results obtained from the analysis of the thermal stresses near the divider lane of a tube sheet from a two-pass heat exchanger.