In planning for health services, the need arises to determine the location, capacity and number of health centers for a geographically defined region. The present paper formulates this problem in a form convenient for solution and presents results from the model to clarify some important aspects of this allocation decision. The planning region is assumed to consist of geographically defined sub areas or census blocks, of known location. The region is stratified in such a way that each stratum exhibits relatively homogeneous patterns of health care utilization. The model characterizes the effects of center locations upon aggregate utilization and utilization of individual centers, and gives optimal locations of centers with respect to several alternative criteria. An example illustrating computational feasibility and the implications of various criteria for the location decision is presented.