Motivated by new sounding-rocket wide-field polarimetric images of the Large Magellanic Cloud, we have used a three-dimensional Monte Carlo radiation transfer code to investigate the escape of near-ultraviolet photons from young stellar associations embedded within a disk of dusty material (i.e. a galaxy). As photons propagate through the disk, they may be scattered or absorbed by dust. Scattered photons are polarized and tracked until they escape to be observed; absorbed photons heat the dust, which radiates isotropically in the far-infrared, where the galaxy is optically thin. The code produces four output images: near- UV and far-IR flux, and near-UV images in the linear Stokes parameters Q and U. From these images we construct simulated UV polarization maps of the LMC. We use these maps to place constraints on the star + dust geometry of the LMC and the optical properties of its dust grains. By tuning the model input parameters to produce maps that match the observed polarization maps, we derive information about the inclination of the LMC disk to the plane of the sky, and about the scattering phase function g. We compute a grid of models with i = 28 deg., 36 deg., and 45 deg., and g = 0.64, 0.70, 0.77, 0.83, and 0.90. The model which best reproduces the observed polarization maps has i = 36 +2/-5 degrees and g ~0.7. Because of the low signal-to-noise in the data, we cannot place firm constraints on the value of g. The highly inclined models do not match the observed centro-symmetric polarization patterns around bright OB associations, or the distribution of polarization values. Our models approximately reproduce the observed ultraviolet photopolarimetry of the western side of the LMC; however, the output images depend on many input parameters and are nonunique. Comment: Accepted to AJ. 20 pages, 7 figures