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The characteristic of steering system is extraordinary critical to vehicle handling and stability, and the coulomb friction, which consist of steering gear coulomb friction and kingpin coulomb friction, are usually neglected in the many previous steering system model. In the paper, the dynamic model of hydraulic power steering system (HPS) including 9 rotational degree-of-freedom (DOF) and 1 translational DOF is presented, taking into account coulomb friction of steering system, and the 2-DOF mathematical model is established based on the manipulation of dynamical theory. Then simulation of vehicle handling stability is developed using the model, a goal of investigation of effects of steering ration, stiffness coefficients and moment of inertia of parts on signs of handling and stability involving yaw rate, slip-angle of center of gravity and lateral acceleration. All the work lay good groundwork for designing and selecting of the parameters of steering system.