Heat pump systems are becoming a popular choice for residential heating and cooling across the United States. Heat pumps are among the cleanest and best energy- and cost-efficient heating and cooling systems available today. However, cost is a prime motivator when choosing among residential heating and cooling systems and it is therefore desirable to analyze the costs associated with heat pump system operation. This research provides a method of direct comparison between the economics of air-source and ground-source heat pump system operation. The objective is to provide a cost comparison with respect to climate locations across the United States, since heat pump performance is heavily influenced by operating environmental conditions such as the ambient air temperature. A purely analytical approach is used for the comparison, avoiding the complexities and costs associated with surveys or experiments, and obtaining actual utility information. Heat pump systems are briefly surveyed, and the thermodynamic operation of vapor compression refrigeration cycles is examined. Analytic models are developed to simulate heating and cooling operation of dual-mode air- and ground-source heat pumps based upon readily available climate data. Finally, a cost ratio relationship is developed to directly compare the associated operating costs for air- and ground-source heat pump systems for a 31 city sample covering much of the continental United States. The annual cost ratio provides the opportunity to evaluate potential cost savings for the operation of air- or ground-source heat pump installations.