Summary: We consider a mathematical model which describes the frictional contact between a viscoelastic body and a reactive foundation. The process is assumed to be dynamic, and the contact is modeled with a general normal damped response condition and a local friction law. We present a variational formulation of the problem and prove the existence and uniqueness of weak solution, using results on evolution equations with monotone operators and a fixed point argument. Then we introduce and study a fully discrete numerical approximation scheme of the variational problem, in terms of velocity variable. The numerical scheme has a unique solution. We derive error estimates under additional regularity assumptions on the data and the solution.