In order to reduce resonant bandwidth and restrict angular displacement, the vibration damping system of an inertial navigation platform should possess tri-directive equal stiffness as far as possible. The disadvantages of traditional placement for rubber dampers are analyzed, and a new placement method for rubber dampers to achieve tri-directive equal stiffness is proposed. This method involves fixing the eight dampers at an incline on the vertexes of the platform. The vibration system is decoupled under such conditions, and tri-directive equal stiffness can be achieved. Numerical simulation is carried out using the finite element model. The results of modal analysis show that with the new placement method, the three translational vibration frequencies as well as the three angular vibration frequencies are almost identical. In addition, the resonant frequencies decrease from 4 to 2, and random vibration analysis indicates that the level of vibration is reduced by 30.09%.