Composite modeling of solids conveying, melting and melt flow in counter-rotating twin screw extrusion is based on combining melt conveying models with melting and solid conveying models. In this paper, 3D non-Newtonian FEM computations have been performed to design the screw pumping characteristics which have been implemented into the composite model of the process. The model has been validated experimentally using a Leistritz ZSE 27HP extruder. Ansys-Polyflow program has been applied to model the melt flow in the machine. An analysis has been performed for the flow in a C-chamber, and the leakage flows have been identified over the calender gap, tetrahedron gap, side gap, and flight gap. Characteristic pressure profiles have been observed with regions of pressure decrease and increase for thick/thin flighted elements, and plateau and linearly declining regions for shearing elements. Screw pumping characteristics have been calculated for various screw elements at various power law indices. It was observed that thick flighted elements have got high pumping capacity which increases with an increase of the power law index, and it is much better than pumping capacity of the thin flighted elements due to positive displacement effect. Shearing elements have got no pumping capacity, and in this case a pressure gradient must be applied to force the fluid through an element, and this gradient increases with an increase of the power law index. It is interesting that a negative pressure gradient has been observed for thick flighted elements for some simulation data. Screw pumping characteristics which are given in terms of dimensionless flow rate and dimensionless pressure gradient, Q*=f(Δp*), have been modeled using regression formulas for various screw elements. These formulas have been implemented into the composite model of the process which has been validated experimentally for LDPE, PS and LDPE/PS polyblend extrusion using a Leistritz ZSE 27HP modular intermeshing counter-rotating extruder.