A multiscale scheme for adhesive elastic contact is proposed to evaluate the interaction mechanisms between two solids. The constitutive law, internal to each body, is described by classical continuum mechanics. The model introduces the atomic structure in the region of contact to evaluate the contact conditions at the coarse scale. Simulations of normal loading and sliding were used to compare quantities such as contact radius, stresses and frictional forces with that from Molecular Dynamics. The radius of contact obtained from the non-adhesive cases show that the model falls in between continuum contact mechanics and molecular dynamics. Stresses resulting from a normal loading are within a few percents of the discrete model for regions further than 15σ from the contact interface. The frictional characteristics exhibit essential stick-slip phenomenon and compare favourably with the Molecular Dynamics results. The integration of the non-linearities of the material at the coarse scale and the account of the out of phase motions of atoms within the coarse scale mesh are necessary to improve the solution in regions subject to more severe stresses.