This chapter presents the dual boundary element method applied to fracture analysis of plates and shells under static and dynamic loading. The dual boundary element method extends the boundary element method to model the behavior of cracks in solids by introducing the integral boundary equation of displacement and tension on either side of the crack faces. In this way, by using both equations simultaneously, the crack can be modeled without the need to define additional conditions at the fracture, which makes it more efficient than other numerical methods based on domain discretization.