The state-of-the-art of stochastic finite element methods is summarized in terms of the uncertainties involved in mechanical structures and discretized according to the finite element division. The pros and cons for the methods proposed so far are discussed briefly. Then the perturbation-based stochastic finite element method is highlighted in conjunction with the evaluation of the rates of change of structural responses and estimation of the response variances due to the input covariance matrix for the probabilistic variables. Recent advances are referred to in regard to the uncertain thermal deformation of an electronic device analysed by the perturbation method and the sensitivity analysis of a spatial piping system with material and support uncertainties.
