The problem of peristaltic transport of a couple-stress fluid has been investigated under a zero Reynolds number and long wavelength approximation. A comparison of the results with those for a Newtonian fluid model shows that the magnitude of the pressure rise under a given set of conditions is greater in the case of the couple-stress fluid. The pressure rise increases as the couple-stress parameter\(\bar \eta \) decreases. The difference between the pressure rise for a Newtonian and a couple-stress fluid increases with increasing amplitude ratio at zero flow rate. However, increasing the flow rate reduces this difference.