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Latin hypercube sampling (LHS) is a popular method for evaluating the expectation of functions in computer experiments. However when the expectation of interest is taken with respect to a nonuniform distribution, the usual transformation to the probability space can cause relatively smooth functions to become extremely variable in areas of low probability. Consequently, the equal probability cells inherent in hypercube methods often tend to sample an insufficient proportion of the total points in these areas. This article introduces Latin hyperrectangle sampling (LHRS), a generalization of LHS that allows for nonequal cell probabilities, to address this problem. A number of examples are given illustrating the improvement of the proposed methodology over LHS with respect to the variance of the resulting estimators. Extensions to orthogonal array-based LHS, stratified LHS, and scrambled nets are also described.