Models are presented for the Ly alpha emission of dusty high-redshift galaxies by combining the Press-Schechter formalism with a treatment of the inhomogeneous dust distribution inside galaxies. It is found that the amount of Ly alpha radiation escaping from the galaxies strongly depends on the time over which the dust is produced through stellar activity, and on the ambient inhomogeneity of the HII regions that surround the ionizing OB stars. Good agreement is found with recent observations, as well as previous non-detections. Although a detailed determination of the individual model parameters is precluded by uncertainties, we find that (i) the dust content in primordial galaxies builds up in no more than ~ 5x10⁸ yr, (ii) the galactic HII regions are inhomogeneous with a cloud covering factor of order unity, and (iii) the overall star formation efficiency is at least 5%. It is predicted that future observations can detect these Ly alpha galaxies upto redshifts of the order of 8. If the universe is reionized at z_r ~ 8, the corresponding decline in the number of Ly alpha emitters at z > z_r could prove to be a useful probe of the reionization.