A stochastic method for sampling spatially distributed contaminant level is presented. The purpose of sampling is to partition the contaminated region into zones of high and low pollutant concentration levels. In particular, given an initial set of observations of a contaminant within a site, it is desired to find a set of additional sampling locations in a way that takes into consideration the spatial variability characteristics of the site and optimizes certain objective functions emerging from the physical, regulatory and monetary considerations of the specific site cleanup process. Since the interest is in classifying the domain into zones above and below a pollutant threshold level, a natural-criterion is the cost of misclassification. The resulting objective function is the expected value of a spatial loss function associated with sampling. Stochastic expectation involves the joint probability distribution of the pollutant level and its estimate, where the latter is calculated by means of spatial estimation techniques. Actual computation requires the discretization of the contaminated domain. As a consequence, any reasonably sized problem results in combinatorics precluding an exhaustive search. The use of an annealing algorithm, although suboptimal, can find a good set of future sampling locations quickly and efficiently. In order to obtain insight about the parameters and the computational requirements of the method, an example is discussed in detail. The implementation of spatial sampling design in practice will provide the model inputs necessary for waste site remediation, groundwater management, and environmental decision making. ¿ American Geophysical Union 1993