We describe radiative transfer calculations of infalling, dusty envelopes surrounding pre-main-sequence stars and use these models to derive physical properties for a sample of 21 heavily reddened young stars (''protostars'') in the Taurus-Auriga molecular cloud. The density distributions needed to match the far-infrared peaks in the spectral energy distributions of these embedded sources suggest mass infall rates similar to those predicted for simple thermally supported clouds with temperatures approximately 10 K. Unless the dust opacities are badly in error, our models require substantial departures from spherical symmetry in the envelopes of all sources, as in Terebey, Shu, & Cassen's rotating infall solutions. These flattened envelopes may be produced by a combination of rotation and cavities excavated by bipolar flows. Terebey, Shu, & Cassen's models indicate a centrifugal radius of approximately 70 AU for many objects if rotation is the only important physical effect, and this radius is reasonably consistent with typical estimates for the sizes of circumstellar disks around T Tauri stars.