This work presents design optimization for a rotor system of a high-speed permanent electrical machine (HSEM), which is commonly used in the field of aerospace, turbomachinery and electrified transportation for high-speed and high-power operations. An optimization methodology incorporating structural vibration and multi-disciplinary constraints was studied to increase the power density and high-speed stability of the machine, integrating the modal analysis, electromagnetic analysis, and the torsional strength analysis of the rotor system. This work utilized dual objective functions for the specific design case of a 24 kW, 12000-r/min electrical machine. The analytical equations verifying the static strength of the rotor system were implemented considering the high-speed operational stability and electromagnetic torque of electrical machine. The electromagnetic model predicting the generated torque of machine was incorporated in the optimization as one of the design constraints. A surrogate optimization algorithm was implemented to search for the optimal results for the multi-objective functions under nonlinear design constraints. A case study on a high-speed PMSM was carried out to demonstrate the effectiveness of the multi-disciplinary optimization methodology, which simultaneously yielded a considerable increase of the motor power density and rotor stiffness.