A new class of potential suitable for modeling the adsorption of water on different metal sites is described. The new potentials are simple in form and convenient for use in computer simulations. In their real space form they comprise three parts : A pairwise sum of spatially anisotropic 12-6 potentials, a pairwise sum of isotropic short range potentials, and an image potential. Two modifications of the potential are developed. In the first, the anisotropic potential acts only on the oxygen atom and not on the protons. In the second, the potential acts on all the atoms of the water molecule. In practical calculations it is convenient to transform the potential to a reciprocal space form in the manner described by Steele [Surf. Sci. 36, 317 (1973)]. Adsorption of water at top, bridge, and hollow sites on (100), (110), and (111) surfaces of Pt, Ni, Cu, and Al were studied using two fitting parameters and the results compared with previous theoretical calculations.