This paper introduces a novel algorithm for delineating mutually exclusive service areas of shelters which have finite capabilities to accommodate residents who are unevenly distributed in space. Minimizing the travel cost and keeping spatial continuity with capability constraint are the convergent objectives of this algorithm. The algorithm partitions an entire residential area into a number of spatial units to handle the unevenness of demand, and employs a shift insertion mechanism to reduce travel cost and to improve the spatial continuity of service areas. A series of experiments and scenarios has been conducted for the city of Memphis, USA, to validate the proposed algorithm. Comparative experiments under different constraints show that the proposed algorithm is a feasible solution for delineating service areas. Various application circumstances (for example, travel-cost calculation methods and the granularity of available demographic data) are discussed to evaluate the algorithm's feasibility. The proposed algorithm can be applied not only to delineating service areas of existing shelters but also to optimizing location allocation of new shelters or other facilities with similar characteristics.