Cumulative distribution functions (cdf) of groundwater model responses are generally determined using Monte Carlo analysis. The procedure consists of (1) generating a number of realizations of the parameters controlling groundwater flow, (2) solving the groundwater flow equation in each of the realizations to obtain the model responses, (3) ranking the model responses, and (4) assigning a probability to each model response as a function of its rank and the total number of realizations. When one is only interested in determining one of the tails of the cdf, e.g., to determine model responses with a small probability of being exceeded, it would be more appropriate to try to reverse steps 2 and 3 above, so that the realizations are ranked first and then the groundwater flow equation is solved only for those realizations leading to responses in the tail of the cdf. Because the ranking of the realizations must be done in terms of their model responses, which calls for the solution of the groundwater flow equation, we propose to use a linear approximation of the flow equation to approximate the ranks. The proposal is based on the conjecture that first-order approximations are more robust for computing the ranks of the piezometric heads than for computing the heads themselves. The conjecture is demonstrated in two two-dimensional confined flow problems comparing the results of the approximation to the results of full Monte Carlo analyses on several sets of 200 realizations with varying standard deviations of log10 T. ¿ American Geophysical Union 1994