This book is dedicated to the understanding of physical and mathematical characteristics of computational solid mechanics by meshless methods. The book reviews and introduces theories, principles, procedures, and formulations that lead to meshless or mesh free methods. It is completely thorough in all derivations. It covers various meshless methods methodologies, provides detailed procedures of meshless analysis of various continuum/solid mechanics problems, including elastostatics, elastodynamics, fracture mechanics, non-local phenomena and plasticity with a large number of numerical examples. The fundamental formulations of continuum mechanics and the finite element methods are also provided in two separate initial chapters to set the stage for the introduction of meshless methods. The inclusion of the chapter in finite element methods (FEM) also provides a ready reference for comparisons, similarities and differences with meshless methods. There are numerous excellent references for finite element methods, and the chapter in this book is by no means a claim for thorough coverage of the FE techniques. The inclusion of the chapter on this topic is due to the encompassing prominence of FE methods in computational solid mechanics. The chapter is intended solely for the methods relevance, contributions, comparisons, and potentials for integration (combination) with meshless methods. The book includes a complete bibliography, ten chapters with several numerical examples, figures, and plots describing computational results, end of chapter exercises/problems in selected sections, and Appendices which provide some fundamental and relevant mathematics required for the reader. A Solutions Manual is available to Instructors. Computer programs for meshless methods covering elastostatics and elastodynamics are introduced in the book and included in an accompanying disc. A complete set of PowerPoint presentations for all chapters are alsoavailable as instructional aid.