We study the Nitsche-based finite element method for contact with Coulomb friction considering both static and dynamic situations. We provide existence and/or uniqueness results for the discretized problems under appropriate assumptions on physical and numerical parameters. In the dynamic case, existence and uniqueness of the space semi-discrete problem holds for every value of the friction coefficient and the Nitsche parameter. In the static case, if the Nitsche parameter is large enough, existence is ensured for any friction coefficient, and uniqueness can be obtained provided that the friction coefficient is below a bound that depends on the mesh size. These results are complemented by a numerical study. (C) 2022 Elsevier B.V. All rights reserved.