The Voyager 2 photopolarimeter (PPS) observed the stars σ Sagitarii and§b Persei as they were occulted by the Uranian ring system on January 26, 1986 (A. L. Lane et al. 1986, Science 233, 65-70). Both occultations passed through the ring system so that orbital radii were sampled at two different longitudes in the ring plane for each occultation. The σ Sagitarii occultation was a grazing occultation and only ε{lunate}, Δ, and 1986U1R occulted the star. β Persei was occulted by each of the nine classical rings twice, and each of these rings was identified on ingress and egress, although the 6 ring in β Per ingress is a marginal detection, and the η ring in β Per ingress was not detected. The orbits of the nine classical rings have been successfully modeled by numerous Earth-based stellar occulations (R. G. French et al. 1988, Icarus 73, 349-378), and Voyager occultation profiles of the rings from the radio science occultation (RSS, D. L. Gresh et al. 1989, Icarus 78, 131-168) and the ultraviolet spectrometer occultations (UVS, J. B. Holberg et al. 1987, Astron. J. 94, 178-188) have been published. The PPS occultations provide high resolution profiles of the rings (∼ 10 m/point for σ Sgr, ∼100 m/point for β Per) which contain information on waves (L. J. Horn et al. 1988, Icarus 76, 485-492), edge sharpness, vertical thickness, and azimuthal variations in radial structure within the rings. The PPS profiles of the ε ring show structure similar to that seen in the radio, UVS, and Earth-based occultations, although the magnitude of peaks and valleys in optical depth changes with azimuth. 1986U1R, γ, η, α, and 6 all show varying degrees of azimuthal inhomogeneity. The η ring is not present in the β Per ingress data although it shows up clearly in egress, and the γ ring is ony 0.6 km wide at β Per ingress and is opaque to the starlight while on the egress cut it is 2.6 km wide. We also present the results of a rigorous statistical search of the data for previously undetected rings. Several features were identified in the β Per data that were more statistically significant than some of the known ring profiles (6 and η in β Per ingress), but the low signal-to-noise ratio for this occultation prevents the identification of any new rings. © 1990.