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We present classical molecular dynamics calculations of the behavior of copper and gold nanoparticles on a graphene sheet, sheared with a constant applied force F_a. The force F_s acting on the particle from the substrate depends on the material of the nanoparticles (Au or Cu), and exhibits a sawtooth dependency on time, which we attribute to local commensurability between the metal nanoparticle surface atomic positions with the graphene lattice. The time-averaged value of F_s (the friction force) acting on Au nanoparticles increases linearly with the contact area, having slopes close to the experimentally observable ones. A qualitative model is proposed to explain the observed results.