The purpose of the book is to introduce the students, geologists, and engineers to the fundamentals of the finite element method and its application in the field of geotechnical engineering with emphasis on rock mechanics. They learn the necessary principles to help them use commercially available programs or to create their own basic finite element code for the stress and deformation analysis of solid structures. The topics covered in this book are: Introduction to numerical methods, displacement Finite element method, equilibrium equations, elasticity relations, formulation procedure (solid mechanics), shape functions, stiffness matrix, load vectors, mesh convergence and accuracy, isoparametric element and numerical integration.