In the long-wave approximation, a theoretical model is developed to describe waves in a rivulet flowing down the lower surface of an inclined cylinder. The model equations are derived by the weighted residual method by projecting the Navier–Stokes equations onto the constructed system of basic orthogonal polynomials. The simplest case of quasi-two-dimensional waves is studied in detail. The stability of the rivulet flow is analyzed and dispersion dependences for linear waves are obtained. The characteristics of nonlinear steady-state traveling waves have been obtained by numerical method for the first time, and the spatial development of forced waves has been studied. The results of calculations are in good agreement with the available experimental data for various liquids in a wide range of parameters.