This paper describes a method to analyze the harmonic components of the air-gap flux density distribution of a 3-phase cage induction motor, by considering the influence of the circumferential slot arrangement, stator winding pattern, and distribution of air-gap permeance by leakage flux. The proposed method is based on an analytical model of the permeance and magnetomotive force distributions. The proposed method is also applied to the analysis of a cage induction motor under starting conditions by considering the leakage-flux magnetic saturation. As a result, the harmonic components of the torque at the starting conditions are shown quantitatively. The proposed method is also confirmed using the numerical analysis method by considering the main flux magnetic saturation. From the comparison of these calculated results, the proposed method is shown to be appropriate and useful for quantitative estimation of the harmonic torque of a cage induction motor.