Based on the hypothesis of continuous medium in theoretical mechanics, the friction resistance model of screw rotary extrusion material was established. The influence of multiple structural parameters of screw on friction resistance was analyzed by using this model, and the range of parameter selection was also given. The friction force between screw and material was the target, and the screw structure parameter was the variable, using Matlab optimization toolbox to optimize the design of screw structure parameters. Moreover, the friction force of the material flow in the optimized screw was analyzed by Ansys. The results showed that the friction stress of the optimized screw was decreased, and the deformation of the screw caused by the material was improved.