Uncertainty in nondestructive elemental or isotopic assay arises from two distinct factors. Unknown spatial distribution of the assayed analyte in the matrix of the sample gives rise to spatial uncertainty. Limitation of the duration of measurement and randomness of the pulse-counting process give rise to statistical uncertainty. These two types of uncertainty occur in the assay of nuclear waste, in mineral prospecting, in in vivo radionuclide assay, and in other applications. In all cases, proper design of the assay system is essential for reliable and accurate assay. The designer of a nondestructive assay system confronts numerous design decisions. He must choose the type and number of detectors to be employed and their arrangement around the sample, the type of radiation to be measured, whether the assay is to be passive or active, and the duration of the measurement. Sometimes the designer is free to specify the shape and size of the sample or the density or composition of the matrix material. A concise, quantitative, computerizable performance criterion is described in detail, which enables the designer to choose from among the wide range of possible assay-system designs. Realistic calculations are presented to illustrate the type of information obtained from the performance criterion.