A clustering problem is one which requires the partitioning of a finite set of objects into subsets so as to optimize a given objective function. The present paper applies such techniques to a well-known set of data on U.S. cancer mortality over the years 1950 to 1967. Two varieties of clustering solutions are obtained: first, states of the United States are clustered according to similarities in their patterns of cancer mortality; then, tumor types are clustered according to mortality similarities over the set of all states. In both, a number of clustering experiments are conducted and these involve the application of a variety of metrics to the raw data, as well as both heuristic and exact solutions of the mathematical problems. The results are displayed graphically, discussed, and in the case of cancer clusters, compared to observed clinical associations.