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This book provides a clear understanding of the nature and theoretical basis of the most widely used numerical methods - the finite element method (FEM) and the boundary element method (BEM) - while at the same time presenting the most promising directions for future developments. Attention is paid mainly to those methods that have proven to be the most reliable and efficient, as well as those methods currently under rapid development. Examples were selected either to illustrate various computational algorithms and compare their accuracy and efficacy or to elucidate the mechanical processes under investigation, while traditional examples that are already covered by standard textbooks have been deliberately omitted. Emphasis is placed on the understanding of basic principles, rather than on the details of individual numerical algorithms. The book covers all topics essential for students of elementary and intermediate courses on numerical methods in solid mechanics, and it also serves as a useful reference for researchers and other professionals. This book was recently translated from the highly regarded, original Czech edition Bittnar and Sejnoha clearly examine the nature and theoretical basis of the most popular numerical methods in structural mechanics - the finite elementary method (FEM) and the boundary element method (BEM), while also presenting the most promising directions for future developments. Outlined are topics essential for students of elementary and intermediate courses on numerical methods in solid mechanics and an overview is given of the most vital areas of current research. The broad selection of examples illustrates various computational algorithms to compare their accuracy and efficiency, or to elucidate the mechanical processes under investigation. Traditional examples covered by standard textbooks have been deliberately omitted. A detailed presentation is offered of the fundamental equations in solid mechanics focusing on constitutive equations including quasibrittle materials. Details are provided on individual numerical algorithms, with a heavier emphasis placed on the understanding of basic principles. Content: 1. Basic Notions, Equations and Principles -- 2. Skeletal Structures -- 3. Plates and Shells -- 4. Solids -- 5. Linear Dynamics and Stability -- 6. Semianalytical Methods -- 7. FE Solution of Special Problems -- 8. Boundary Element Method -- 9. Problems of Nonlinear Mechanics -- 10. Adaptive FE Techniques -- 11. Systems with Random Fields -- A. Matrix Formulation of Gauss Elimination -- B. Numerical Integration. Abstract: This work has been written to provide an understanding of the nature and the theoretical basis of the most widely used numerical methods - the finite element method (FEM) and the boundary element method (BEM), and, at the same time it outlines the most promising directions of their future development. 3 Read more... Bittnar and Šejnoha explain the nature and theoretical basis of the most widely used numerical methods—the finite element method and the boundary element method—and present the most promising directions for future developments.