Fluid flows within microchannels are characterized by low Reynolds numbers. Therefore the effect of mixing is a crucial factor in design of the channels. Since the action of the electro-osmotic or magnetic forces used in the mixing enhancement is usually periodic in the three-dimensional channel configuration, use of the various concepts of chaotic advection is reasonable in the quantification of the stirring effect. In this paper, the details of the method of material-stretching mapping is explained. The actual application of the method to the screw extruder is also presented.