Extrusion is recognized as the key process in single-base gun propellant manufacturing. Uniform propellant columns obtained through extrusion are placed in the extrusion cylinder, where a pressure difference is established by a hydraulic press. The propellant material is extruded through the forming die into strips. As a viscoelastic solid, the propellant material exhibits velocity non-uniformity at the die exit during extrusion. This results in excessively high flow rates in individual channels and critically low flow rates in others. Insufficient flow rates cause solvent evaporation and material drying in the affected channels, leading to channel blockage. Based on the rheology of viscoelastic solids, a flow dynamics model of the propellant material within the die is established in this study. The conservation equations are solved using the Finite Volume Method. The influence of inlet velocity on the mean value and uniformity of the outlet flow is analyzed. Results indicate that as the inlet velocity increases, the mean outlet velocity demonstrates an increasing trend. Regarding outlet uniformity, a gradual deterioration followed by rapid degradation is observed. Therefore, selecting a higher inlet velocity within an acceptable velocity variance range not only ensures process safety but also maintains production efficiency. This work aims to provide a theoretical basis for predicting and improving the safety of single-base gun propellant extrusion processes.