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In this research the effect of the screw angle and the depth of the channel were examined on the flow rate of an incompressible Newtonian isothermal and a non-Newtonian fluid flow in a single screw extruder. In the presented study the pressure drop has not been considered and only drag force was considered. For this purpose, the channel of extruder was assumed a cubic and spiral channel. Accordingly the Newtonian flow was simulated by Fluent foftware package and the results were compared with analytical solution in several angles. Then one step from the shallow spiral channel was examined and the results were compared with analytical solution in different angles and also at low Reynolds numbers. Hence, the obtained results reveal the range of validity for the analytical solution at different Reynolds numbers. As the results show, at low Reynolds numbers, up to 10, and the ratio of channel depth to diameter, less than 0.2, numerical and analytical results are the same for Newtonian fluids. Identically in this range the analytical solution can be used for screw design, calculation of the maximum flow rate, the evaluation of the optimum angle, etc. The results of the study of non-Newtonian fluid showed that the flow rate at low screw angles for non­-Newtonian fluids were higher than the Newtonian cases and at high angles, were smaller.