The modeling and nature of the physisorption of water at the metal (Hg)-water interface is explored in this paper. We have evaluated potential models that fit into three general classes that are employed in the literature. These classes are distinguished by the manner in which the isotropic interactions between the metal and the water are modeled : namely, as non-attractive, weakly attractive, and strongly attractive. In the present studies the metal is described by a jellium model. In our model, in addition to the isotropic water potential there is an interaction between the jellium and the water molecules which depends on the orientation of the water molecule with respect to the metal surface. We find that hard potentials without isotropic attractive terms dewet. The density of water near hydrocarbon-like potentials remains close to the bulk value but the interaction isn’t strong enough to structure the water near the interface, nor are the adsorption energies sufficiently high. The strongly attractive potentials seem to be the most appropriate. For such models we have checked the sensitivity of the results to the parameters in our model including surface corrugation. We find that the structural results are insensitive to the parameters employed suggesting that they not only provide a good classical description of the Hg-water interface but may be readily adaptable to describe the physisorption of water on metals in general. Although we find the layering of water molecules and the pattern of hydrogen bonding near these surfaces, which have been described as ice-like in previous studies, the actual arrangement of the water molecules near these surfaces is distinctly different from the structure of ice.