The paper describes the design and analysis of Radioisotope Thermoelectric Generators Integrated with JPL's planned Solar Probe spacecraft. The principal purpose of the Solar probe mission is to explore the solar corona by performing in-situ measurements at distances as close as four solar radii or 0.02 AU from the sun. This proximity to the sun Imposes some unusual design constraints on the RTG and on its integration with the spacecraft, principally with respect to dissipation of the generator's waste heat to space. A number of schemes for achieving this without excessive performance penalties were examined, and the preferred schemes were analyzed in detail. Since these entail obstructed and highly unsymmetrical heat rejection paths, they required development of a novel analytical approach and computer code for performing coupled thermal and electrical analyses of RTGs with axial and circumferential temperature, current, and voltage variations. The code was validated against measured test data of unobstructed RTGs, and was used for the detailed analysis of highly obstructed RTGs for the Solar Probe mission. The results demonstrated that the obstructions result in significant performance penalties for the case of the standard GPHS-RTG design. IVIodiflcations of that design to reduce those penalties are under investigation. Finally, the paper describes a simple empirical method for predicting the combined effect of fuel decay and thermoelectric degradation on the RTG's power output, and applies that method to predict the long-term power profile of the obstructed Solar Probe RTGs. The results indicate that the existing GPHS-RTG design, even without modifications, can meet the JPL-prescribed EOlVI power requirement.