Conditions under which equations of state (EOS) are valid are investigated by calculating implicit interatomic potentials for fixed structures. Third-order Eulerian finite strain yields physically realistic potentials only for ~3.8'0rd order yields reasonable interatomic potentials for the range K'0 commonly occupies. Potentials for 4th order are unrealistic if K'0 varies by more than a few % from the 3rd order value. Vinet, Ferrante, Rose and Smith's EOS should be used instead for materials with high K'0 (e.g., gases or liquids) because it yields valid potentials for all values of the elastic parameters. ¿ American Geophysical Union 1993