Dimensionless nonlinear vibration equations of tilted support spring system under dropping condition were established. The dynamic equations were solved by using Runge-Kutta method. The influence of dimensionless dropping impact speed, the support angle of system, and damping ratio on the system response were discussed. The result showed that the maximum shock response displacement and the maximum shock response acceleration increases with increasing of dimensionless dropping impact speed; with decreasing of support angle, the maximum shock response displacement increases and the maximum shock response acceleration decreases; damping ratio has significant influence on the system response and optimum damping ratio exists for the maximum shock response acceleration, which decrease with decrease of support angle. It was concluded that impact resistance of system can be enhanced effectively by suitable selection of damping and the angle of the system.