Using the embedded atom method (EAM), we have calculated the stable configurations of Pt, Pd, and Ni clusters, containing up to nine adatoms, on the Pt (001) surface. For Pt, we predict that the stable configurations are linear chains oriented along the <110> directions for three and five adatoms, and close-packed islands otherwise. These results, for clusters containing up to seven adatoms, were reported previously in reference 4. For Pd, the results are the same except that the stable configuration predicted for five adatoms is a close-packed island. For Ni, we predict that linear chains are the stable configurations for all numbers of adatoms. In determining these stable configurations, we allowed substrate relaxations. To assess the importance of substrate relaxations, we also performed calculations on an unrelaxed substrate. We found that substrate relaxations are important with regard to the stable configurations, and that allowing relaxation lowers the energies of chains with respect to islands.