Abstract In this article, the mechanism of cilia-induced flow is discussed through a mathematical model. In this analysis two-dimensional flow of a viscous fluid is observed in a curved channel with ciliated walls. The features of ciliary structures are determined by the dominance of viscous effects over inertial effects using the long-wavelength approximation. The flow is modeled in both fixed and wave frame references. The exact solution is calculated for the velocity profile and the flow properties for the viscous fluid are determined as a function of the cilia and metachronal wave velocity. Results for the pressure rise, pressure gradient and stream function are constructed and analyzed graphically.