By analyzing the principle of FA transmission and its structural characteristics, taking FA45-29 reducer as the research object, and the three-dimensional model of simplified model of the prototype is built and virtual assembly is carried out without interference. By importing Hypermesh for detailed mesh generation, contact definition and constraint addition, the finite element model is established, and then importing ANSYS for modal analysis under constraint conditions. The natural frequencies and mode shapes are obtained, which not only avoids complex theoretical modeling and calculation, but also lays a foundation for the subsequent dynamics analysis and rigid-flexible coupling analysis. At the same time, it provides a theoretical basis for the evaluation of the dynamic performance of FA reducer, the design of experimental scheme and the structural optimization design of all parts of the reducer.