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A copper or another high-conductivity shield is often used for coating the solid rotor for reducing the armature-reaction space and time-harmonic-induced surface eddy-current losses in a solid-rotor synchronous machine. Since finite-element-simulation-based surface-loss evaluation for shield design can be very time consuming and complicated; a simple analytical model for calculating the surface losses is derived in this paper. A set of equations is derived based on Maxwell's equations for a general case and applied to a solid-rotor synchronous machine. Simulation results are provided to show that the proposed analytical model can serve as an effective screening tool for determining the optimal shield thickness for minimizing the rotor surface losses. The model is useful for assisting the shield-design process for synchronous machines with solid rotors, especially for high-speed machines operating in conjunction with power electronic converters.