Stability of midpoint algorithm applied on solving the equation of motion with nonlinear damping is analyzed by using conservation of energy in this paper. Bilinear model, a special case of the nonlinear damping, is also discussed in stability analysis of this algorithm. nonlinear computation of one SDOF model and two MDOF models are finished to check the reliability of the proof progress. From the studying property of the nonlinear equation, theoretic basement is given for numerical stability, in addition we can draw the conclusion that midpoint scheme is one of the best methods for this nonlinear problem.