Abstract: An approximate method is presented for obtaining analytical solutions for the conditional first passage probability of systems under modulated white noise excitation. As the method is based on VanMarcke's approximation, with normalization of the response introduced, the expected decay rates can be
evaluated from the second-moment statistics instead of the correlation functions or spectrum density functions of the response of considered structures. Explicit solutions to the second-moment statistics of the response are given. Accuracy, efficiency and usage of the proposed method are demonstrated by the first passage analysis of single-degree-of-freedom (SDOF) linear systems under two special types of modulated white noise excitations.