The paper firstly numerically simulates the coupled model of triangle fastening screw threads in the application of ANSYS software. Calculate stress intensity of the screw thread on the axial pressure of 200MPa. The fittest coupled turn number of the screw nut is designed to make sure the strength of coupled teeth and make every turn of the screw thread go on very well and also save material. The maximum equivalent stress of the screw thread changes linearly with the axial pressure. The stress of the thread's root is greater than that of the thread's top so that the root is easily damaged. The paper's research method can apply to the optimal design of the other patterns of screw thread's turn number.