||The problem of reliability analysis of randomly parametered, linear (or) nonlinear, structures subjected to static and (or) dynamic loads is considered. A deterministic finite element model for the structure to analyze sample realization of the structure is assumed to be available. The reliability analysis is carried out within the framework of response surface methods which involves the construction of surrogate models for performance functions to be employed in reliability calculations. This construction, in the present study, has involved combining space filling optimal Latin hypercube sampling, kriging models and methods from data-based asymptotic extreme value modeling of sequence of random variables. Illustrative examples on numerical prediction of reliability of a ten-bay truss, a W-seal in an aircraft structure, and a nonlinear randomly parametered dynamical system are presented. Limited Monte Carlo simulations are used to validate the approximate procedures developed.