A simple asymptotic model of a stationary rotationally symmetric flow in an infinite cylindrical channel with irregular walls is constructed and investigated. We assume that kinematic viscosity is depends on the radial and axial coordinates. The kinematic condition corresponding to the impermeability of the boundary for the liquid is chosen. It is assumed that the classical non-slip condition is completed only in straight segments of the boundary. For parts of the boundary that are not straight, any additional terms, in addition to the kinematic conditions, not required. It is shown that at any fluid flow rate in domains where the curvature of the cylinder boundary is negative, there are toroidal vortices in the stationary flow. The solution of the problem is constructed in analytical form. This solution is valid in any domain with sufficiently smooth cylinder boundaries. As an example, we consider the case of turbulent kinematic viscosity vanishing at the cylinder boundary. To prevent the velocity singularities the roughness of the wall is introduced. The proposed model can simulate the blood flow through the vessels and, in particular, be used to study the quasi-stationary motion of impurities, for example, erythrocytes, in the flow with the known structure.