A sharp-interface two-phase numerical analysis is performed for co-current downward laminar flow of a liquid film and a gas. A complete two-phase model based on the two-dimensional elliptic governing equations is presented. The numerical model implements a dynamically moving non-orthogonal computational mesh that tracks the phase interface precisely. The capability of this new model is demonstrated by comparisons with two previous free surface falling film studies and one experiment. New results are presented on the effect of independent variation of the Reynolds and Froude numbers on the axial variation of the film free surface. Finally, the effects of the velocity of the gas phase on the liquid film development are examined for flow in a parallel-plate channel. An analytical solution for the fully-developed velocity profiles for the two-phase flow is also presented.