An extensive study has been presented on the polymer melt flow in a closely intermeshing counter-rotating twin screw extruder. A fully three-dimensional non-Newtonian FEM computations have been performed to design the screw pumping characteristics which may be implemented into the composite model of the process. ANSYS Polyflow software has been applied to model the melt flow in the machine. An analysis has been performed for the flow in the C-chamber, and the leakage flows have been identified over the calender gap, tetrahedron gap, flight gap, and side gap. Screw pumping characteristics have been calculated and modeled for screw elements at various power law indices. It has been observed that a thick flighted element due to the positive displacement effect has got high pumping capacity increasing with an increase of the power law index. A shearing element has got no pumping capacity, and in this case a pressure gradient must be applied to push the material through an element, and the gradient increases with an increase of the power law index. Negative pressure gradient has been observed for thick flighted elements at some simulation data, and a respective reorientation of the velocity flow field has been seen.