According to poor computational accuracy at small to median sample sizes of Monte Carlo ( MC ) simulation techniques in estimating the probability failure of mechanical structures, the number theoretical net ( NT-net ) simulation method is proposed to reduce computing effort. Several key concepts, such as good point set, good-lattice point ( glp ), discrepancy and NT-net method, are defined. The sampling stategy is improved by introducing NT-net that can provide better convergent rate over MC. The new method is used to estimate failure probability of the side impact bar on the car door. Results indicate the computational effort needed by NT-net for the same accuracy is about 1/12 of that needed by the MC-based method, and the obtained results are more stable.