The application of the saddlepoint approximation to reliability analysis of dynamic systems iS investigated.The failure event in reliability problems is formulated as the exceedance of a single performance variable over a prescribed threshold level.The saddlepoint approximation technique provides a choice to estimate the cumulative distribution function (CDF) of the performance varilable.The failure probability is obtained as the value of the complement CDF at a specified threshold.The method requires computing the saddlepoint from a simple algebraic equation that depends on the cumulant generating function(CGF) of the performance variable.A method for calculating the saddlepoint using random samples of the performance variable is presented.The applicable region of the saddlepoint approximation is discussed in detail.A 10-story shear building model with white noise excitation illustrates the accuracy and efficiency of the proposed methodology.