Abstract: The analysis of elastic buckling of random structures using recursive stochastic finite element method(RSFEM)is presented.Buckling eigenvalues and eigenvectors of random structures are expressed as non-orthogonal polynomial expansions that are randomly convergent.Utilizing perturbation technique,a set of deterministic recursive equations are set up.Statistic buckling eigenvalues of structures are obtained by iteratively solving the deterministic equations.It is found in numerical examples that compared with perturbation stochastic finite elements method based on Taylor expansion,the results of RSFEM are more close to those of Monte-Carlo simulation in large range of random fluctuation.The examples also show that acceptable results can still be obtained using RSFEM with only the first four orders of non-orthogonal polynomial expansions.