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The paper considers the vertical channel of a regular packing for a falling-film apparatus with a countercurrent gas flow. The mathematical problem of the motion of a gravitational film with a countercurrent gas flow is formulated on the basis of the Navier Stokes equation. The mathematical problem includes, the steady flows in the vertical channel of a circular cross-section, a laminar motion of a smooth film is considered, which include the equality of tangential stresses on the boundary between the phase, the condition of adhesion on a solid surface. This mathematical problem is solved analytically, the given solution results allow us to estimate the local velocities of the falling-film and a countercurrent gas flow. An experimental stand with working channel was used for the experimental verification of mathematical results. The working channel like a double pipe has a height of 1 m and internal / external tube diameters of 17/36 mm. A test experiment determines the thickness of the falling-film and compares this to the Nusselt formula. Accuracy of test experiments on an experimental stand -up to 15%. Several series of experiments were carried out under the condition of the laminar-wave regime of falling-film and the laminar motion of air Re film / Re air = 200/2150. The deviation of the experimental results for the local velocities of the phases from the results of the solution of the mathematical problem increases with the growth of phase velocities and makes up 19-30% for the laminar-wave mode of motion of the film in the vertical channel of the contact apparatus. The proposed solution of mathematical problem determines the local velocities in the vertical coaxial channel of the falling-film apparatus and allows to provide high accuracy of local velocity calculation at the laminar air movement. [ABSTRACT FROM AUTHOR]