Today the fundamentals of solid mechanics may be explained by "numerical" experiments using the finite element method. The explanation is detailed in this book using many examples. After a short review of how the finite element method works (in Chapter 1), Chapter 2 develops some key points of solid mechanics: what is a beam? when and how can a structure be represented by beam elements? what are the basic hypotheses? what kind of information does a beam model provide? A generalized beam element is also presented. Chapter 3 uses the same approach for the discussion on stress concentrations and stress singularities: local effects; influence of geometric discontinuities, such as holes or corners; mesh refinements and/or analytic-numeric approaches. Chapter 4 is devoted to plate modeling: coupling of membrane and bending, folded, stiffened, composite plates. Chapter 5 provides a short presentation of the dynamics of structures with a particular focus on the modal method, the influence of local defaults on the modal response is also analyzed. Commercial software (Ansys) is used to study the examples.