We estimate the distribution of apparent axis ratios q for galaxies in the Sloan Digital Sky Survey Early Data Release. We divide the galaxies by profile type (de Vaucouleurs vs. exponential) as well as by color (u* - r* ≤ 2.22 vs. u* - r* > 2.22). The axis ratios found by fitting models to the surface photometry are generally smaller than those found by taking the second moments of the surface brightness distribution. Using the axis ratios found from fitting models, we find that galaxies with de Vaucouleurs profiles have axis ratio distributions that are inconsistent, at the 99% confidence level, with their being a population of randomly oriented oblate spheroids. Red de Vaucouleurs galaxies are slightly rounder, on average, than blue de Vaucouleurs galaxies. By contrast, red galaxies with exponential profiles appear very much flatter, on average, than blue galaxies with exponential profiles. The red exponential galaxies are primarily disk galaxies seen nearly edge-on, with reddening due to the presence of dust, rather than to an intrinsically red stellar population.