Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions comprehensively covers the theoretical background of asymptotic approaches and its applicability to solve mechanical engineering-oriented problems of structural members, primarily plates (statics and dynamics) with mixed boundary conditions. The first part of this book is devoted to the description of asymptotic methods, and also includes coverage of lesser known, but useful approaches including the method of summation and construction of the asymptotically equivalent functions, methods of small and large delta, homotopy perturbations method, etc. The second part of this book deals with the application of the asymptotic methods to solve various problems of the theory of plates with mixed boundary conditions. Both free and forced vibrations of plates, as well their stress-strain states and stability problems are studied. The results are presented in a simple analytical form, and can be directly used in engineering practice. It describes the state-of-the-art of current asymptotic approaches. It deals with new trends and applications of asymptotic approaches in the field of Nonlinear Mechanics and Mechanics of Solids. It uses detailed examples from the field of non-linear mechanics and civil engineering. It presents a rigorous treatment of the homotopy perturbation technique.