The flexible polarizable AMOEBA force field for water is tested with classical molecular dynamics simulations from ambient up to supercritical conditions. Good results are obtained for the heat of vaporization, dielectric constant, self-diffusion constant, and radial distribution functions provided densities are fixed at the experimental values. If instead the densities are allowed to relax to those characteristic of the liquid gas equilibrium for the model, then satisfactory results are obtained near ambient conditions, whereas at high temperatures the liquid densities are generally underestimated and the gas densities overestimated. As a consequence, the critical point of the model is reached at significantly too low temperature, although it occurs at approximately the correct density.