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An analysis describing the peristalsis of non‐Newtonian fluids in a symmetric channel is carried out. Two explicit forms of Phan‐Thien‐Tanner model are used in the flow description. Mathematical analysis is presented at small Reynolds number and large wavelength assumptions. The influence of emerging parameters is highlighted upon the pressure rise, frictional force, and shear stress. In addition, pumping phenomena is described. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 737–748, 2012