Understanding of the growth, stability, and structural properties of coherently strained metal overlayers has achieved considerable importance because of the recent discovery of unique interfacial electronic states and catalytic properties of such systems. The structural stability of coherently strained metal films grown on a substrate composed of a different and lattice-mismatched metal is determined via atomistic calculations. An equilibrium energy balance criterion is used, which is evaluated with a Monte Carlo annealing optimization procedure in which the structural energy of the bimetallic system is obtained using the embedded atom method. The stability of coherently strained (100) bimetallic structures chosen from combinations of the fcc metals Ag, Au, Cu, Ni, Pd, and Pt has been studied. The predicted critical thicknesses agree remarkably well with experimental results, but disagree quantitatively with the continuum models.