Air motion problems in ventilation systems of buildings, underground facilities (mines, the underground), etc. can be simulated by means of the motion of an incompressible homogeneous viscous fluid. The aim of this work is to develop a method of solving stationary traffic in the channel of an incompressible homogeneous viscous fluid with the given pressure at the inlet and outlet of the channel and to study the stability of the solutions. (C) 2013 Elsevier Ltd. All rights reserved.