This book provides mechanical engineering students with the theoretical and fundamental basics of the Finite Element (FE) method used in structural mechanics. Students should be able to apply this knowledge to develop FE models and use them to analyze systems both statically and dynamically. The author believes that learning about the Finite Element tool without learning how to build computer codes for it makes it just a theoretical tool, good only for very simple models with very few elements, rather than being useful for practical problems. In most of the chapters of this book, computer codes using MATLAB are presented in order to render the developed models useful for practical applications. Moreover, the book also stresses on the idea that engineers should be able to convert real life problems into simplified models from which one can predict the behavior or the performance of the system.