The development of precast concrete housing systems provides an opportunity to easily and inexpensively incorporate solar energy collection by casting collector tubes into the roof structure. A design is presented for a precast solar water heating system used to aid in meeting the space and domestic water heating loads of a single family residence. A three-dimensional transient collector model is developed to characterize the precast solar collector's performance throughout the day. The model describes the collector as a series of segments in the axial direction connected by a fluid flowing through an embedded tube. Each segment is represented by a two-dimensional solid model with top boundary conditions determined using a traditional flat plate solar collector model for convection and radiation from the collector cover plate. The precast collector is coupled to a series solar assisted heat pump system and used to meet the heating needs of the residence. The performance of the proposed system is compared to the performance of a typical air to air heat pump. The combined collector and heat pump model is solved using Matlab in conjunction with the finite element solver, Femlab. Using the system model, various non-dimensional design and operating parameters were analyzed to determine a set of near optimal design and operating values. The annual performance of the near optimal system was evaluated to determine the energy and cost savings for applications in Atlanta, GA and Chicago, IL. In addition, a life cycle cost study of the system was completed to determine the economic feasibility of the proposed system. The results of the annual study show that capturing solar energy using the precast collector and applying the energy through a solar assisted heat pump can reduce the electricity required for heating by more than 50% in regions with long heating seasons. The life cycle cost analysis shows that the energy savings justifies the increase in initial cost in locations with long heating seasons but that the system is not economically attractive in locations with shorter heating seasons. / Master of Science