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In order to reduce the computational cost of engineering analysis in the reliability assessment of structures, the response surface method (RSM) has been widely used in the literatures. This work examines the application of support vector machine (SVM) to the reliability assessment of structures. A new SVM based RSM is proposed for structural reliability assessment, in which an efficient sampling method has been designed to generate the training data based on Gauss-Hermit integral points and variable transformation. The proposed approach is investigated by two examples to validate its accuracy and efficiency. It is found that the SVM based RSM is more efficient and accurate than the conventional polynomial based RSM.