The paper is devoted to a theoretical analysis of a viscous liquid film flowing down a vertical one-dimensional periodic surface. The investigation is based on both Navier-Stokes and integral equations and performed over a wide range of Reynolds number and surface geometry characteristics taking into account viscosity, inertia and surface tension. Shape of the film free surface and streamline function are calculated. It is shown that there are two ranges of parameters where the film flow is controlled by surface tension or inertia forces and where qualitatively different behavior of the flow main characteristics is obtained. Stagnation zones are found and their transformation with increasing Reynolds number is investigated. Comparison with experimental data is carried out.