Methane and water demix under normal (ambient) pressure and temperature conditions because of the polar nature of water and the apolar nature of methane. Recent experimental work has shown, though, that increasing the pressure to values between 1 and 2 GPa (10-20 kbar) leads to a marked increase of methane solubility in water, for temperatures which are well below the critical temperature for water. Here, we perform molecular dynamics simulations based on classical force fields-which are well-used and have been validated at ambient conditions-for different values of pressure and temperature. We find the expected increase in miscibility for mixtures of methane and supercritical water; however, our model fails to reproduce the experimentally observed increase in methane solubility at large pressures and below the critical temperature of water. This points to the need to develop more accurate force fields for methane and methane-water mixtures under pressure.