The nonlinear dimensionless dynamical equations of tilted support packaging system considering vulnerable part were established, and the numerical analysis of vibration response of vulnerable part was carried out using Runge-Kutta method. The effects of the angle of the tilted support, the frequency ratio and mass ratio of the system on the response of acceleration and displacement were discussed. It was shown that the effects of the angle of tilted support and the frequency ratio of the system are particularly noticeable; increasing frequency ratio of the system can obviously decrease the maximum response acceleration and displacement of vulnerable parts; the peak of vibration response of vulnerable parts can decreased at low frequency ratio by increasing mass ratio. The purpose was to provide academic foundation for design of shock absorber with tilted support.