In order to study the probability distributions on the dynamic responses of the uncertainty ceramic thermal protection system (TPS), a double random dynamic theoretical model for uncertainty TPS under the outer random excitations is presented in this paper. In the theoretical model, the tile is simplified as a mass point, the strain isolation pad (SIP) is simplified as a linear spring and a damping unit, and the above mass point, the stiffness of spring and the damping all obey the normal distribution. The probability distributions for acceleration of the tile and the dynamic stress of SIP are studied by a perturbation method, and the key problem is to obtain the sensitivity analysis of the mean responses to the random parameters of TPS. The theoretical method and Monte Carlo numerical method are used to calculate the probability distributions of responses. The results show that the mean values and standard deviations of the responses calculated by theoretical method match very well with that calculated by Monte Carlo numerical method, which verifies the correctness and analysis accuracy of the dynamic theoretical model presented in this paper. Finally, the works in this paper provide a theoretical basis for the analysis of the uncertainty acceleration of tile, the uncertainty dynamic strength of SIP and the uncertainty dynamic integrity of TPS.