Electronic Journal of Differential Equations, Vol. 2006(2006), No. 156, pp. 1-7. Title: Elasto-plastic torsion problem as an infinity Laplace's equation Authors: Ahmed Addou (Univ. Mohammed premier, Oujda, Maroc) Abdeluaab Lidouh (Univ. Mohammed premier, Oujda, Maroc) Belkassem Seddoug (Univ. Mohammed premier, Oujda, Maroc) Abstract: In this paper, we study a perturbed infinity Laplace's equation, the perturbation corresponds to an Leray-Lions operator with no coercivity assumption. We consider the case where data are distributions or $L^{1}$ elements. We show that this problem has an unique solution which is the solution to the variational inequality arising in the elasto-plastic torsion problem, associated with an operator $A$. Submitted October 11, 2006. Published December 18, 2006. Math Subject Classifications: 35J70, 35J85, 74C05. Key Words: Infinity Laplace equation; elasto-plastic torsion problem; variational inequality.