This book addresses the  problems of fracture mechanics of materials with cracks under the loading directed along the cracks. It considers two non-classical fracture mechanisms, namely the fracture of bodies compressed along cracks and the fracture of materials with initial (residual) stresses acting in parallel to the surfaces of cracks location, and presents new approaches (also including combined one) developed in the framework of three-dimensional linearized mechanics of deformable bodies. It then discusses the results of studies on two- and three-dimensional problems for various configurations of crack locations in isotropic and anisotropic materials, and based on these results, critically evaluates the accuracy and applicability limits of the “beam approximation” approach, which is widely used to study various problems of the fracture of bodies under compression along parallel cracks.