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, Chapter 2 develops some key points of solid mechanics. Chapter 3 focuses on stress concentrations and stress singularities. Chapter 4 is devoted to plate modeling. 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.