Site characterization is an important prerequisite of risk assessment and remediation strategies. Evaluation of the health effects of groundwater and soil contamination depends on the adequate analysis of spatial heterogeneity, exceedance levels, and uncertainties. In this work we formulate and calculate stochastic indicators that provide a rigorous characterization of exposure levels in sites with heterogeneous contaminant distributions and offer valuable information for a cost-effective cleanup analysis. These site indicators are general and can be used for different types and distributions of groundwater and soil contaminants. Important properties of the stochastic indicators are examined which can evaluate the potential for contamination at large scales, and improve understanding of threatened and damaged ecosystems. Analytically tractable formulas are derived that allow the practical estimation of site indicators on the basis of experimental data. Scale and modeling effects on contaminant level analysis are examined in terms of the stochastic indicators. Site cleanup costs depend directly on inferred characteristics of the stochastic indicators, which thus can play an important role in waste site management. Applications are discussed that offer insight regarding certain aspects of stochastic site characterization. Analytical methods of site characterization are compared to numerical simulations. It is shown that the latter can provide a practical alternative to the former, but they could lead to inaccurate results if they are not interpreted carefully. ¿ American Geophysical Union 1996