In this research, the Supercavitation phenomenon in compressible liquid flows is simulated. The one-fluid method based on a new exact two-phase Riemann solver is used for modeling. The cavitation is considered as an isothermal process and a consistent equation of state with the physical behavior of the water is used. High speed flow of water over a cylinder and a projectile are simulated and the results are compared with the previous numerical and experimental results. The cavitation bubble profile in both cases agrees well with the previous experimental results reported in the literature. As the result shows, coupling the two-phase Riemann solver with the considered EOS prepares a robust method for simulating the compressible fluid flow with cavitation which can undertake the whole physical behavior of water in a supercavitation process. Furthermore, the influence of the cavitator head and the flow speed on the supercavitation bubble is explored. The results show that cavitators with sharper head results in a smaller supercavitating bubble. Increasing the flow speed beyond a specific limit does not have any significant effect on the cavitation bubble and slightly increases the bubble size.