An efficient numerical simulation method for the evaluation of global sensitivity analysis with parameter uncertainty, Appl. Math. Modelling (2015), doi: http://dx.Abstract: For structural systems with both epistemic and aleatory uncertainties, an efficient numerical simulation method is proposed to evaluate the effect of epistemic uncertainty on failure probability measured by the variance based sensitivity analysis. The direct evaluation of the effect needs a "triple-loop" crude sampling procedure and is time consuming. To circumvent the difficulty associated with the direct sampling based procedure, an improved importance sampling (IS) method is first constructed, and further the improved IS based procedure is proposed for efficient evaluation of the effect of epistemic uncertainty. The core of the proposed method is to construct the same IS probability density function (PDF) for failure probability corresponding to individual realization of epistemic uncertainty. Using the proposed improved IS based method, only an IS run with a set of input-output IS samples is needed to determine the estimated values of the effects for all epistemic uncertainties. Several examples are employed to demonstrate the feasibility of the proposed method for different situations. Examples show that the proposed method can ensure a reasonable accuracy of results with less evaluations of performance function compared with the available methods.