Regarding high-speed permanent magnet machines (HSPMMs), there is a lack of complete and detailed design processes for main parameters under multiphysics constraints, which makes it difficult to obtain high-reliability designs for designers of HSPMMs. This paper presents a detailed and complete design process for the main parameters of an HSPMM under multiphysics constraints. Firstly, the initial sizes are obtained through electromagnetic and mechanical design theory. Then, the influence of design parameters on rotor stress is analyzed in detail, including PM material, rotor temperature, sleeve thickness, PM thickness and rotor diameter. Furthermore, the rotor dynamics have also been studied in detail, including the effects of bearing stiffness, impeller mass, rotor diameter, core length, and gyroscopic effect on critical speed. Afterwards, the comprehensive research on the electromagnetic filed and the loss characteristics is performed. The cooling system is designed and the thermal field is also studied in Ansys-Cfx. Besides, the coupled temperature-stress analysis is established considering the interaction between temperature and mechanical characteristics. Finally, a full-size HSPMM prototype has been fabricated and tested to validate the detailed multiphysics design process.