During the recent years, the use nonlinear finite element method has become a normal practice not only for University researchers, but also for many engineers working, for example, on design and analysis of failure. Affordable commercial nonlinear finite element softwares and more powerful and inexpensive computers have made possible this. It is unquestionable the importance and impact of the use of computer modelling in engineering. Despite this, it has been observed that many of the people, who use these programs, frequently lack of the necessary knowledge of some concepts on the nonlinear theory of elasticity. As a result, it was considered necessary to have a text, which would provide a simple, but as complete as possible, an overview of some basic topics on the theories of non-linear, linear elasticity and finally on the nonlinear finite element method. This book is intended as an introductory textbook on solid mechanics, elasticity and the nonlinear finite element method, and it is only required to have some basic knowledge on vector calculus, partial differential equations, and tensor analysis.