A numerical reservoir model which simulates three dimensional, three phase flow through porous media is presented. The model is based on the numerical solution of the equation of conservation of mass for each phase. The state of phase equilibrium is determined by oil and gas formation volume factors and gas solubility. All the fluid properties are considered to be functions of pressure only. In order to solve the resulting matrix equation, the Alternating-Direction method is used. With this model, a two-dimensional simulation of the depletion drive of an oil reservoir, and a three-dimensional simulation of an oil reservoir with a weak water drive were simulated. The necessary time to calculate one time step-block was arround 0.0216 seconds by IBM 360-75 system.