In the design field of straight conjugate hydraulic pump gear,due to the lack of efficient meshing geometry model, it is difficult to obtain the meshing rule of gears and guide the design of tooth profile by using the existing theory. In order to solve this problem, an accurate meshing geometric model was established based on Willis theorem and inversion method. A classical internal meshing gear was taken as an example, the specific formulas of meshing lines were deduced, the geometric design methods for meshing lines and conjugate lines were given, and the correctness of the design was verified by simulation.Based on SolidWorks software, the dynamic assembly simulation of the geometric model was carried out to study its internal meshing law.The meshing problem of straight conjugate gears design can be solved by using the accurate geometric model. It provides reference for the design of straight conjugate gears