In this work we consider a solid body $\Omega\subset{\Bbb R}^3$ constituted by anonhomogeneous elastoplastic material, submitted to a density of body forces $\lambda f $ and a density of forces $\lambda g$ acting on the boundary where the real $\lambda $ is theloading parameter.The problem is to determine, in the case of an unbounded convex of elasticity, the Limitload denoted by $\bar{\lambda}$ beyond which there is a break of the structure. The case of a bounded convex of elasticity is done in [El-Fekih and Hadhri, RAIRO: Modél. Math. Anal. Numér. 29 (1995) 391–419]. Then assuming that the convex of elasticity at the point x of Ω, denotedby K(x), is written in the form of $\mbox{K}^D (x) + {\BbbR}\mbox{I}$ , I is the identity of ${{\Bbb R}^9}_{sym}$ , and thedeviatoric component $\mbox{K}^D$ is bounded regardless of x $\in\Omega$ , we show under the condition “Rot f $\not=0$ or g is not colinear to the normal on a part of the boundary of Ω", that theLimit Load $\bar{\lambda}$ searched is equal to the inverse ofthe infimum of the gauge of the Elastic convex translated bystress field equilibrating the unitary load corresponding to $\lambda =1$ ; moreover we show that this infimum is reached in asuitable function space.