This chapter presents the mechanical models and approximations by the FEM for problems of plane stress,
plane strain, and twist of noncircular cross-sections. We also discuss the compatibility conditions, the Airy
function for the construction of solutions to linear elastic plane problems, analytical solution of three-
dimensional problems, the (hp)2FEM software for high-order approximation, and examples of ﬁnite element simulation of three-dimensional models. We consider the generalization of numerical integration rules for two-
and three-dimensional domains. At the end, we present a summary of the variational formulation of mechanical
models considered in this book. This chapter is mainly based in references [51, 30, 36, 38, 22, 25, 13].