Finite Element Methods For Engineers is designed to serve as a textbook for a first course in the finite element method (FEM) for undergraduate and postgraduate students of engineering. It provides an insight into the theory and application of FEM. The book introduces the reader to FEM as a mathematical tool and covers the application of the method to mechanical and civil engineering problems. Beginning with an introduction to calculus of variations, the book goes on to describe Ritz and Galerkin FEM formulations and one-, two-, and three-dimensional FEM formulations. Application of the method to bending of beams, trusses, and frames, and problems of plane stress and plane strain, free vibration, plate, and time history are also included. Discussions on advanced topics such as FEM formulation of flow problems, error analysis in FEM, and non-linear FEM make for a complete introductory text. Inclusion of topics such as approximation methods for solving differential equations, numerical integration, and methods for solving FEM problems on a computer enhance the utility of the book. The book has been written in a simple and comprehensible manner to enable students to grasp important concepts easily. A number of solved problems and illustrations (in colour where required) have been incorporated to aid in the study of relevant topics. A large number of objective questions and exercises have also been included to test the students’ understanding of FEM and its applications.