Abstract This paper deals with the reliability analysis of a complex structural system, in which the failure of the system is due to plastic collapse. Of particular interest herein is the computation of the time-variant probability of the structural system failure under nonstationary load processes. The theoretically most attractive approach for this type of problem in time-dependent structural reliability analysis is to employ the concept of first passage probability in stochastic process theory. Because the use of the generalized Rice formula poses some difficulty, the outcrossing problem will be formulated herein in another way, i.e., using the original Rice formula directly. This situation allows the multidimensional integral to be reduced to a one-dimensional integral. Also it can include smooth nonstationary processes as well as time-variant domain boundaries. An example is given to illustrate the method.