We developed a Monte Carlo code that describes the resonant Ly$alpha$ line transfer in an optically thick, dusty, and static medium. The code was tested against the analytic solution derived by Neufeld (1990). We explain the line transfer mechanism by tracing histories of photons in the medium. We find that photons experiences a series of wing scatterings at the moment of thier escape from the medium, during which polarization may develop. We examined the amount of dust extinction for a wide range of dust abundances, which are compared with the analytic solution. Brief discussions on the astrophysical application of our work are presented.