AbstractIn this paper, an iterative method of statistic linearization (IMSL) is presented to solve non‐linear stochastic vibration equations. This method represents an improvement over the classical linearization method. The method uses the solution of the corresponding linear vibration equation as an initial value in an iterative procedure. To obtain information about essential statistical average values, the method uses a ‘boot‐strapping’ procedure, which defines a pseudorandom process based on the statistical characteristics of the linear solution and then uses samples from the process to estimate them. For Gaussian input excitation, the statistical average values are obtained by theoretical a