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This monograph focuses on research into methods for predicting reliability of randomly parametered structures, subjected to random dynamic loads. Specific themes explored include the development of multivariate extreme value distributions and their applications in time variant reliability analysis of structural systems, extreme value distribution of non-Gaussian random processes, such as the Von Mises stress metric, development of response surface methods for time-variant reliability analysis involving performance functions with multiple design points and/or multiple regions of comparable importance and issues related to discretization of non-Gaussian random fields in the context of stochastic finite element analysis of random dynamical structures. A case study on the seismic fragility analysis of the piping network in a nuclear power plant using the developed methods has been presented as an appendix. Some sample programs relevant for the developed methods and for interfacing reliability codes with a commercially available finite element software are also included as appendices. The monograph consists of seven chapters and three appendices.