The aim of this paper is to study the existence of solutions for some quasilineare anisotropic elliptic problem associated with differential inclusion. We study the two cases of
 <i>f&in; L<sup>&infin;</sup>(&Omega;)</i> and <i>f&in; L<sup>1</sup>(&Omega;)</i>. Moreover, we show the uniqueness of solution under some additional assumptions.