Abstract: An analytical model is developed for a spur gear pair with an addendum modification to concern the tip relief when calculating time-varying mesh stiffness, by considering the effects of nonlinear contact stiffness, of revised fillet-foundation stiffness and of extended tooth contact. The proposed model is verified by the finite element (FE) method. The ranges of optimum parameters for tip relief are acquired by making the sum of the first five-step amplitude of fast Fourier transform (FFT) for mesh stiffness minimum. Furthermore, stress analysis is conducted to prove the optimal modification parameters based on the FE method. Results showed that the design method based on the sum of the first five-step amplitude of FFT for mesh stiffness minimum can determine efficiently the optimal modification parameter range and the stress analysis based on the finite element method can further verify the optimal parameters of tip relief. The fluctuation of stiffness and stress decrease obviously after tip relief, which can contribute to the reduction of vibration and noise in the meshing process of gear pairs. The results can provide a theoretical basis for the tip relief design of a spur gear pair with an addendum modification.