First， the models of tooth with root cracks are classified into three types according to the relation between the distance from the crack tip to the centerline of a tooth and half of the tooth thickness. For each model， the expression of meshing stiffness changed with the crack depth is derived based on the energy method. Then， the meshing stiffness are analyzed by the finite element method to prove that the proposed models are effective. Finally， the dynamic model of gear system is established based on the expressions of meshing stiffness to analyze the vibration response of the gear system. The results show that the meshing stiffness decreases as the depth of crack increases. The deeper the crack is， the faster the stiffness decreases. When the parameter that represents the crack depth is larger than 50%， the stiffness decreases sharply. The vibration response intensifies and suffers the periodic impact as the crack depth increases . Furthermore， when the frequency is close to the meshing frequency， small clutters occur， the trajectory in the phase diagrams extends and the aggregation region of discrete points in the Poincare diagrams expands.