In pressure vessels and piping the leak-before-break (LBB) assessment method is employed to avoid any catastrophic failure prior to a detectable leakage. One of the most important parameters, the leak rate, is investigated in the present paper by means of the Monte Carlo method. A brief reviewed is carried out with emphasis on aspects such as crack growth, crack size with detectable leakage, crack opening area and leak rate. Issues concerning the property and behavior of multiple cracks are also covered along with a review of the characteristics of leak rate through distributed multiple cracks using a statistical simulation method. The simulation results show that, the effect of multiple cracks is quite significant to the LBB concept. Both the relationship between leak rate and crack length (or time) and the statistical characteristics of the leak rate are considerably different for different initial crack conditions.