A three-dimensional multi-phase flow is simulated around a smooth tire. This simulation is conducted by solving Navier-Stokes equation with a k-$varepsilon$ turbulent model. The numerical calculations are carried out by modeling a multi-phase free surface flow mixed with air and water at the inlet. The numerical solutions show an intuitively resonable behavior of water around a moving tire. The calculated pressure around the tire surface along the moving direction is presented. The moving velocities of the tire are chosen to be 30, 40, 60, and 70 km/h. The numerically simulated pressures around the tire are compared with existing experimental data. The comparison shows a new possible tool of analyzing a hydroplaning phenomenon for an automobile tire by means of a computational fluid dynamics.