In this paper we deal with a class of inequality problems for static frictional contact between a piezoelastic body and a foundation. The constitutive law is assumed to be electrostatic and involves a nonlinear elasticity operator. The friction condition is described by the Clarke subdifferential relations of nonmonotone and multivalued character in the tangential directions on the boundary. We derive a variational formulation which is a coupled system of a hemivariational inequality and an elliptic equation. The existence of solutions to the model is a consequence of a more general result obtained from the theory of pseudomonotone mappings.