Calculations are performed for the creation and transport of linearly polarized maser radiation in the presence of Faraday depolarization due to free electrons. Attention is limited to magnetic field strengths for which the characteristic Zeeman splitting gΩ is much less than the spectral line breadth Δω—the regime that ordinarily is appropriate for astrophysical SiO, H2O, and CH3OH masers. Analytic solutions are obtained for unsaturated masers though numerical methods must be utilized when there is radiative saturation. The investigation here is motivated by observations of the differences in the fractional linear depolarization between the J = 3-2, 2-1, and 1-0 transitions of circumstellar SiO masers. These data have been interpreted as suggestive of Faraday depolarization, with potential implications for the magnetic field strengths and fractional ionizations in these environments. For comparison with observation, the emphasis is on the relationship between the fractional polarization and the position angle of the polarization vector. The changes in position angle that we calculate for Faraday depolarization exclude this interpretation. Most likely, the observed variations in the fractional polarization are due to a combination of (1) differences in the degrees of saturation, (2) the detailed effect of anisotropic radiation on the multilevel network of the rate equations that govern the molecular populations, and (3) the competitive gain among the various masing transitions.