Nonlinear plate and shell analysis has significant application in the analysis of thin-walled structures, such as those found in the aeronautical industry. The nonlinear problems addressed in this chapter relate to deflection problems in elastic plates and shells with large deflections and small strains, which allows for the analysis of post-buckling behavior. Similarly, the analysis of plates with elastoplastic response considering small deflections and strains represents another large group of nonlinear problems in the study of plates and shells. This chapter is presented as an introduction to nonlinear problems in BEM. The topics presented here are advanced topics in BEM, and their study is left to the reader in the bibliographical sources provided.