In high-speed solid-rotor induction machines, space harmonics in the air gap flux density corresponding to the stator slots typically cause significant losses on the rotor surface. Since these slot harmonics rotate very fast with respect to the rotor, their corresponding skin depths are typically very small. Loss estimates obtained by transient finite-element (FE) analysis may, therefore, require very fine spatial and temporal discretization and consequently very long solution time. In this paper, we derive a time-harmonic analytical model for the multilayer cylindrical rotor. Since the effect of the stator slots on the eddy-current losses cannot be ignored, the analytic solution is coupled to a numerical FE solution covering the stator. The resulting method is very fast since time stepping and meshing of the rotor can be avoided. The results are compared to those obtained with full 2-D transient FE analysis.