This paper presents solution methods for elastoplastic and shakedown a
nalysis of linearly elastic, perfectly plastic bodies for which the co
nventional classical formulations of these problems are completed by c
onstraints on overall plastic deformation and elastoplastic displaceme
nt. The methods are described in terms of nonlinear mathematical progr
amming and provide solutions when the plastic reserves of the body are
not fully exhausted, and the plastic performance and the plastic defo
rmations are controlled. Application of the method is illustrated by a
n example.