We model both the total power and the degree of circular polarization as measured by the Planetary Radio Astronomy (PRA) experiment on the Voyager spacecraft. A new model defines the instrument response to an incident wave of arbitrary polarization and direction. For the planetary source, we postulate the location and the emission mode. Knowing the location and attitude of the antennas, we model the direction and polarization of the received wave. The two models together predict the time variation of total power and of polarization for direct comparison with PRA data. The limiting polarization of the propagating wave is estimated for the modeled Uranian sources and found to be similar to the polarization at the source. The instrumental response is calculated for the initial polarization of the incident wave. The smooth Uranian emission at 58.8 kHz is interpreted as X mode emission near the gyrofrequency. Emission cones, symmetric about the magnetic field direction, originate at source elements which are distributed in longitude at a given magnetic latitude. The sense of polarization and the total power can be modelled by either wide-angle, hollow emission cones from equatorial source elements or narrow, filled cones from conjugate sources at moderately low latitude. The degree of polarization is modelled more closely by filled cones from conjugate sources than by wide hollow cones on the equator. Quantitative modeling of polarization provides a new tool for thorough analysis of planetary radio emission observed by PRA.