This study of the problem of the equilibrium of a perfectly plastic body under specific conditions employs tools and methods that can be applied to other areas, including the mechanics of fracture and certain optimal control problems. The three-part approach covers variational problems in plasticity theory, solution of variational problems in the finite-energy spaces, and asymptotic problems and problems in the theory of plates. Includes a new Foreword by the author. AUTHOR: Roger Teman is Director of the Institute for Scientific Computing and Applied Mathematics at Indiana University. He was previously on the faculty of the University of Paris-Sud from 1967–2003. A member of the French Academy of Sciences he was also elected to the American Academy of Arts and Sciences in 2015. His many books include Mathematical Modelling in Continuum Mechanics and Navier-Stokes Equations.