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This text discusses the basics of the finite element method in a simple and systematic way. The book can serve as a basic learning tool for undergraduate and postgraduate students in civil and mechanical engineering whose main interest is to carry out stress analysis. However, the concepts are presented in sufficiently general form, that the book can also be used as a valuable learning aid for students with other backgrounds, and by practising engineers. Key features: The finite element method described with examples of bar and CST element. Includes a chapter on shape functions with large number of examples. Isoparametric elements and numerical integration are explained in detail. Advanced topics on plate and shell elements, non-linear problems and dynamic analysis are covered. Isoparametric elements with explanation of input, output, test example and source code are included in the CD appended to the book. Detailed appendices on the Rayleigh-Ritz method, solutions to equations and numerical integration.