Abstract A modified computational scheme of the stochastic perturbation finite element method (SPFEM) is developed for structures with low-level uncertainties. The proposed scheme can provide second-order estimates of the mean and variance without differentiating the system matrices with respect to the random variables. When the proposed scheme is used, it involves finite analyses of deterministic systems. In the case of one random variable with a symmetric probability density function, the proposed computational scheme can even provide a result with fifth-order accuracy. Compared with the traditional computational scheme of SPFEM, the proposed scheme is more convenient for numerical implementation. Four numerical examples demonstrate that the proposed scheme can be used in linear or nonlinear structures with correlated or uncorrelated random variables.