An analytical solution is obtained for the flow in a simplified model of the shallow single screw extruder of polymer melts described by the simplified Phan-Thien-Tanner fluid with linear kernel function. To arrive at the analytical solution in the rectangular channel, both the effects of the channel curvature and of the spanwise coordinate are neglected in the flow (shallow channel/extruder) and the fluid properties are considered to be temperature-independent. The two Couette-Poiseuille flows are coupled via the nonlinear constitutive equation and the results are presented in dimensionless form as a function of all relevant dimensionless numbers. The results show that as shear-thinning is enhanced there is a decrease in the ratio between the strengths of the main and secondary flows and in the dimensionless pressure rise through the extruder. (C) 2011 Elsevier B.V. All rights reserved.