Abstract: Referring to the orthogonal expansion & random function of stochastic processes, the probabilistic model of non-stationary ground motion processes is established, and the earthquake ground motion can be represented using a basic random variable. The representative discrete point set of the basic random variable can be selected, and the representative sample ensemble for non-stationary ground motion processes can be directly generated by the probabilistic model. The proposed earthquake probability model provides an opportunity to employ the probability density evolution method (PDEM) to study the stochastic nonlinear responses and seismic reliability of general structural systems. An example, which deals with a non-linear MDOF Duffing system subjected to random earthquake excitations, is investigated to validate the above approach.