Monte Carlo simulations have been performed in the Np(N)AT statistical ensemble to study the methane-water mixture as a function of pressure. The interfacial tensions are calculated with different definitions and are reported for pressures from 1 to 50 MPa. The interfacial tensions, coexisting densities, and composition of the methane and water phases are shown to be in good agreement with the corresponding experimental properties. The interfacial region has been described through the profiles of the number of hydrogen bonds, the coordination number of each species, and the different energy contributions. We complete this study by a theoretical investigation of the thermal and mechanical equilibria in the binary mixture. We have also examined the profile of the intrinsic and long range correction parts of the interfacial tension along the normal to the water surface.