Most dynamic systems have various random properties m excitation and system parameters. In this paper, a procedure for structural response and reliability analysis is proposed for the linear dynamic system with random properties in both excitation and system parameters. The system parameter and response with random properties are modeled by the perturbation technique, and then the response analysis is formulated by probabilistic and vibration theories. Probabilistic FEM is also used for the calculation of mean response which is difficult by the proposed response model. The first passage analysis by the integral equation method is used to analyze the probability of failure. The integral equation method results in the first passage probability in terms of crossing rates and first passage probability densities. In this study it is assumed that excitations, system parameters and responses are Gaussian. As an application example, the probabilities of failure at transient state are calculated for a sdof system with random mass and spring constant subjected to stationary white-noise excitation and the results are compared to those of numerical simulation.