A nonlocal finite element model is developed for solving elasto-static frictional contact problems of nanostructures and nanoscale devices. A two dimensional Eringen-type nonlocal elasticity model is adopted. The material is characterized by a stress-strain constitutive relation of a convolution integral form whose kernel is capable to take into account both the diffusion process of nonlocal elasticity and the scale ratio effects. The incremental convex programming procedure is exploited as a solver. Two examples of different nature are presented, the first one presents the behavior of a nanoscale contacting system and the second example discusses the nano-indentation problem.