There are currently no precise P-V-T data for water at pressures above 8.9 kbars and temperatures above 900°C. Many petrological processes in the lower crust and upper mantle take place under more extreme conditions, however and petrologists commonly rely on empirical equations of state such as the modified Redlich-Kwong equation (MRK) to extrapolate the low pressure data. In this study we have taken an alternative approach and attempted to simulate the P-V-T properties of water using molecular dynamics. The TIP4P intermolecular potential for H2O (Jorgensen et al., 1983) has had considerable success predicting the properties of water at low temperatures and pressures up to 10 kbar (Madura et al., 1988). We have extended its application by making molecular dynamics (MD) simulations at a density of 1.0 g/cc from 300 to 2300 K and 0.5 to 40 kbars. The results agree with the P-V-T data of Burnham et al. (1969) (up to 10 kbars) with an average error of under 2%. This is a much better concordance than is obtained with any of the currently used versions of MRK. At 300 kbars and 2000 K the MD simulations predict densities within 8% of those obtained in the shock wave experiments of Kormer (1968). This is a very good agreement given the fact that water ionizes to some extent at high pressures (Mitchell and Nellis, 1982) and we have made no provisions for this effect. We conclude that molecular dynamics simulations provide the possibility of estimating P-V-T properties in the upper mantle P-T regime with very good accuracy.