This chapter presents the theories used throughout the book for isotropic and laminated materials for plate and shell analysis, both thin and thick, using the boundary element method. For thin plates, the classical theory of linear elastic plates based on Kirchhoff’s hypotheses is presented, along with its extension to the case of thin shells. In both cases, the mechanical hypotheses governing their behavior are presented, and their governing equations are developed. Likewise, the thick plate theory, or Reissner-Midlin theory, is presented in the case of isotropic elastic thick plates. The extension of this theory to the case of laminated plates is given through the first-order shear theory. Their extension to developing the governing equations for isotropic thick shells and laminated material is presented for both cases. The governing equations presented here are again presented in their corresponding chapter on the application of the method so that each chapter is self-contained as much as possible.