The radiation dose rates resulting from airborne activities inside a postaccident pressurized water reactor containment are calculated by a discrete ordinates / Monte Carlo combined method. The calculated total dose rates and the skyshine component are presented as a function of distance from the containment at three different elevations for various gamma-ray source energies. The one-dimensional ANISN code is used to approximate the skyshine dose rates from the hemisphere dome, and the results are compared favorably to more rigorous results calculated by a three-dimensional Monte Carlo code.