Using step in the hull of planing vessel is one of the ways for resistance reduction. This step can be placed in the bottom of the planing vessel in order to change the height of it. By using this step a further lift force at the bottom of hull is occurred which is lead to improvement of planning vessel motions and decreasing in the wetted surface, consequently the lift force is decreased at the high velocities. High speed planning vessels may lose their stability during movement however they have a sufficient static stability. This insatiability can be attributed to roll, pitch, yaw, oscillating motion, heeling the planing vessel to right or left, compounding motions and other parameters. In this thesis, turbulent two-phase flow around the hull of one step planing vessel is simulated in the calm water with non-zero heel by using navier stokes, equation of rigid body motion and morphing mesh. In order to ensure the accuracy of the simulation, the simulation is carried out for a non-step planing vessel by steady state condition and non-zero heel firstly. The obtained results of this first simulation such as lift force, moment of heel and wetted surface is validated and compared with the experimental data. At the continue, the simulation is done for a one step planing vessel which the system has two degree of freedom. The results of the resistance force, sinkage, dynamic trim, wetted length of the chine and length of the wetted keel at the different velocities are compared and validated by using the experimental data which is available in the literature. Also this thesis gives a discussion about the separation length after the step of the planing vessel and variation in the spray angle at the different velocities. After ensure about the accuracy of the simulation in the two mentioned steps, the numerical simulation is extended to a one-step planing vessel with the non-zero heel and some hydrodynamic properties is predicted for planing vessel. The governing equations a