Abstract: This paper discusses numerical integration methods considering the geometric nonlinear equation of motion, and compares the difference between the average acceleration method (AAM) and the energy conserving method that presented by M.A.Crisfield. Based on co-rotational technologies, the nonlinear finite element program is written. The reliability of the program is verified by comparing the analytical and numerical solutions of a simple pendulum. The dynamic analysis of a planar truss structure and a commonly used space structure show that the energy of AAM is unbounded with a larger time interval, while the response of the energy conserving method is always stable with different time intervals. Therefore, we suggest that the energy conserving method should be more suitable for the dynamic computation with geometric nonlinearity.