This paper introduces a new approach for the design and analysis of nonlinear stress-grading systems for high voltage rotating machines. The method is based on the simulation and modeling of stress-grading systems using a nonlinear lumped circuit model. The nonlinear model is analyzed in the time domain using the describing function method. The model generates the time variation of the resistances as well as the surface electric field and potential and ultimately converges to the optimal design parameters of the stress-grading system. The model is iterative and adaptive where a deviation from the nominal uniform field and the upper and lower bounds on the resistance values as well as bounds on the nonlinearity factor can be set to generate optimal design parameters of the stress-grading system.