A mathematical model describing the quasistatic process of frictional contact between a nonlinearly elastic body and an elastic-rigid foundation is considered. The contact is modeled by normal compliance with unilateral constraint, and the friction by a slip-dependent version of Coulomb’s law. A weak formulation of the problem is derived and, under a smallness assumption on contact and friction functions, an existence result is proved by using incremental techniques, Kakutani’s fixed point theorem, and compactness, monotonicity, and lower semicontinuity arguments.