Abstract: Cauchy-inequality is utilized to analyze and evaluate the variance of the simulation result of the Monte Carlo method with importance sampling technique involved. The concept of medium probability is introduced and the relationship between medium probability and simulation result variance is deduced. And based on this conclusion, the sampling function which will minimum the simulation result variance is figured, and cirque and semi-cirque intercepting tail importance sampling methods, as importance sampling techniques, are built. Especially, the ratio between the sampling function to the original distribution function is constant in the methods and the sampling points distribute in a spherical space, which take the origin as a center and the distance from the origin to the limit state surface as a radius. Furthermore, the quantitative description for the reduction of variance of simulation results can be obtained. The results of example and analysis indicate that the variance of simulation results by cirque and semi-cirque intercepting tail importance sampling methods can be reduced to one tenth and one twentieth of that by a direct method.