Abstract: In this paper, the nonlinear damping which depicts the exciting process on the initial stage is adopted. After the rupture velocity reaches its maxium value, decaying process succeeds.We obtain the analytical solution for the mode Ⅲ dynamic rupture subjected to the nonlinear Rayleigh damping. First, the Galileo transformation is adopted to transform the fixed coordinates into moving coordinates.Then the unknown function is assumed to be Fourier series in moving coordinates with coefficient as functions of time variable only. Applying the orthognality of Fourier series, the nonlinear PDE of the governing equation is reduced into two infinite systems of nonlinear ODEs. By successive approximation method, the analytical solution is obtained.