This book is aiming to concentrate on the nonlinear static and dynamic analysis of structures and structural components that are widely used in everyday engineering applications. It approaches a nonlinear problem by mathematically converting it into an exact equivalent pseudolinear one, in contrast to commonly used approaches which are based on linear concepts. The new concepts, theories and methods introduced in this book, simplify a great deal the solution of the complex nonlinear problems, and also allow for the correct usage of the powerful existing linear methods of analysis. Based on this way of thinking, the book also provides a reasonable treatment regarding the nonlinear analysis of inelastic plates, suspension bridges and their failures, multistory buildings subjected to strong earthquakes, as well as many other interesting nonlinear problems, such as thick cylinders, inelastic torsion, inelastic vibrations, inelastic analysis of flexible members, and many more.