Abstract: In this paper, Monte-Carlo method is used for thereliability analysis of elastic plane problems, in which the splinefictitious boundary element method (SFBEM) is used as the sample experimentapproach due to its high accuracy and efficiency. In order to furtherimprove the calculation, Taylor expansion and Neumann expansiontechniques are adopted to avoid generating influence matrices and theirinverses during the repeated calculations of a large number of sampleanalyses, and the calculation time of a single sample analysis isconsiderably reduced. In addition, an important sampling method is alsoused to reduce the sampling numbers while the same accuracy ismaintained. Numerical results show that the proposed method, theTaylor-Neumann expansion important sampling Monte-Carlo SFBEM, canachieve a good accuracy and a relatively high efficiency for thereliability analysis.