Abstract: Aiming at the problem of temperature rise and components deformation of an axially spherical bearingless flywheel machine(AS-BFM), the magnetic-thermal-solid coupling analytical method is proposed. The electromagnetic loss of AS-BFM is analyzed, and the thermal parameters and stress parameters of AS-BFM components are established. Then, a three-dimensional finite element analysis model of AS-BFM is built, and the loss and temperature field distribution characteristics of AS-BFM at different speeds are obtained. Further, the results of the temperature field are imported into the stress field analysis as a load to solve the components deformation. Finally, the influence law of the temperature rise and components deformation under different speeds of AS-BFM has been revealed by coupling simulation analysis, and three-dimensional finite element simulation results verified the validity of the proposed magnetic-thermal-solid coupling analysis method, which laid the foundation of heat dissipation design, structural optimization and material selection of AS-BFM.