Fragility curves represent the conditional probability that a structure's response may exceed the performance limit for a given ground motion intensity. Conventional methods for computing building fragilities are either based on statistical extrapolation of detailed analyses on one or two specific buildings or make use of Monte Carlo simulation with these models. However, the Monte Carlo technique usually requires a relatively large number of simulations in order to obtain a sufficiently reliable estimate of the fragilities, and it is computationally expensive and time consuming to simulate the required thousand of nonlinear seismic analyses. In this paper, High Dimensional Model Representation (HDMR) based response surface method together with the Monte Carlo Simulation is used to develop the fragility curve, which is then compared with that obtained by using Latin Hypercube sampling. It is used to replace the algorithmic performancefunction with an explicit functional relationship, fitting a functional approximation, thereby reducing the number of expensive numerical analyses. After the functional approximation has been made, Monte Carlo simulation is used to obtain the fragility c urve of the system.