We study misfit dislocations in a two-dimensional elastic lattice model of epitaxy using Green's function. The interaction between the dislocations of the lattice model is compared with that of continuum elasticity theory. It is found that the behavior of the lattice model at a long distance agrees with that of standard continuum theory, but an additional interaction between dislocations due to extra forces around the dislocation core is important. The extra forces also lead to an increase in the dislocation interval. On a flat adsorbate surface with a periodic array of misfit dislocations, the preferential adsorption site is found to be either on the top or at the midpoint of the dislocations depending on the sign of the force dipole moment of the adatom and the sign of the misfit parameter.