The book gives a synthetic presentation of the research performed in the field of sheet metal forming simulation during more than twenty years by the members of three teams: the Research Centre on Sheet Metal Forming a " CERTETA (Technical University of Cluj-Napoca, Romania); AUTOFORM software-house company from ZA1/4rich, Switzerland and VOLVO automotive company from Sweden. The first chapter reminds some fundamental topics of the theory of plasticity. A more extended chapter is devoted to the presentation of the phenomenological yield criteria, emphasizing the formulations proposed by the CERTETA team (BBC models). The sheet metal formability is discussed in a separate chapter. After presenting the methods used for the formability assessment, the discussion focuses on the forming limit curves. In this context, the authors emphasize their contributions to the mathematical modeling of forming limit curves. The aspects related to the implementation of the constitutive models in finite-element codes are discussed in the last chapter of the book. The performances of the models are proved by the numerical simulation of various sheet metal forming processes: hydroforming, deep-drawing and forming of the complex parts. The book is useful for the students, doctoral fellows, researchers and engineers who are mainly interested in the mechanical modeling and numerical simulation of sheet metal forming processes. modeling and numerical simulation of sheet metal forming processes.