Almost half of primeval galaxies show P-Cygni type profiles in the Ly$alpha$ emission line. The main underlying mechanism for the profile formation in these systems is thought to be the frequency re-distribution of the line photons in expanding scattering media surrounding the emission source. A Monte Carlo code is developed to investigate the Ly$alpha$ line transfer in an optically thick and moving medium with a careful consideration of the scattering in the damping wings. Typical column densities and expansion velocities of neutral hydrogen investigated in this study are $N_{H1}{~}10^{17-20};cm^{-2}$ and ${Delta}V{~} 100 km;s^{-1}$. We investigate the dependence of the emergent profiles on the kinematics and on the column density. Our numerical results are applied to show that the damped Ly$alpha$ absorbers may possess an expanding H I supershell with bulk flow of ${~}200 km;s^{-l}$ and H I column density $N_{H1}{~}10^{19};cm^{-2}$. We briefly discuss the observational implications.