Multiple scattering of polarized light in a birefringent turbid plane medium was studied using a Monte Carlo simulation. The reduced effective scattering Mueller matrix obtained in the simulation was factorized in two dimensions using the Lu-Chipman decomposition, yielding polarization parameters that exhibited dependences on the azimuth and the radial distance around the illumination point. We propose a double-scattering model for the propagation of polarized photons in turbid infinite plane media. When the birefringence slow axis is along the azimuth of 90° on the plane surface, the retardance becomes the largest negative along the azimuth of 0° and the largest positive along the azimuth of 90° and increases with increasing the azimuth from 0° to 90°. This azimuthal dependence may result from the overlap of the contributions from the light propagations vertical to, and lateral along, the plane surface. Thus, the dependences on the azimuth and the radial distance of the polarization parameters, such as the retardance, its orientation, optical rotation, and the depolarization coefficients, are correctly predicted.