An accurate, and efficient computational procedure is proposed for structural reliability analysis. The suggested advanced Monte-Carlo simulation utilizes the concept of conditional integration which takes into account the shape of limit-state functions in the generation of samples. An efficient computational scheme to determine approximate analytical limit-state functions, from which the samples will be generated, is also suggested for those cases where no analytical limit-state function is available. Numerical examples show the applicability of the proposed procedure to analyze structural systems in terms of failure probability.