This book describes the main concepts of and recent advances in the base forces element method (BFEM). It combines theories, methods, models, numerical results, and an analysis of the BFEM. Each chapter starts with an introduction and derivation of a new mathematical model for the proposed method. Subsequently, the methods are described and numerical examples demonstrating the significance of the proposed method are presented. The closing chapter summarizes the performance and features of the BFEM and describes the prospects for its application. The book is intended for engineers, scientists and graduate students in applied mechanics and applied mathematics, and for all readers interested in numerical computations and simulations.