The random seismic loading and structural hysteretic restoring force model commonly used were summarized in this paper. The analysis method commonly used for random vibration of nonlinear systems, including the diffusion theory method, the stochastic averaging method, perturbation meth-od, the moment truncation method,digital simulation method and the equivalent linearization method were discussed. The theory, development and the application of the method of equivalent linearization in hysteretic structures with random seismic response analysis were summarized. The results showed that the equivalent linearization method, especially in recent years, the local equivalent linearization method and no parameters equivalent linearization method,random seismic response of a hyste一retie structure can be analyzed in a very simple and practical way. By exploring random equivalent lineari- za-lion method of error analysis and correction, we can get the conclusion that the use of equivalent lineariz一ation method can lead to highly accurate results. This paper is of a certain reference value for the seismic reli一ability of reinforced concrete structure analysis method.