In this paper, we analyze a quasistatic problem modeling frictional contact between a viscoplastic body and an obstacle, the so called foundation. The material constitutive relation is assumed to be non-linear. The boundary conditions of contact and friction are modeled respectively by the \textit{Signorini} conditions and the generalized Coulomb's non-local law. We derive a variational formulation for the problem and prove the existence of its unique weak solution. The proof use, essentially, classical arguments of compactness, variational inequalities and Banach’s fixed point theorem.