Summary: Peristaltic pumping by a sinusoidal travelling wave in the wall of a two-dimensional channel filled with a viscous incompressible couple-stress of a magneto-fluid is investigated theoretically and graphically. A perturbation solution is obtained which satisfies the momentum equation for the case in which the amplitude ratio is small. The results show that the mean axial velocity decreases with increasing couple-stress parameter \(\eta\) and magnetic parameter \(M\). The phenomenon of reflux is discussed. Numerical results are reported for various values of the physical parameters.