This manuscript proves the existence and regularity of solutions with respect to the summability of second member ∈ L m(·) (Ω), to the obstacle problem associated to nonlinear elliptic equation −div A(x, v, ∇v) = in Ω, u = 0 in ∂Ω. (1) The arguments are based on the rearrangement techniques to obtain some priori estimates in Marcinkwicz spaces with variable exponents.