A reliability-groundwater flow analysis is performed and the influence of flow parameters on the probability of exceeding the threshold value is examined. For this study, the 3-D numerical groundwater flow program, DGU-FLOW, is developed by extending the 2-D flow program and is coupled to the first and second order reliability program. The 3-D flow program is verified by solving the examples of groundwater flow through the underground excavation and comparing the results from commercial MODFLOW program. Reliability routine of the program is also verified by comparing the probability of failure with that of Monte-Carlo Simulation. The reliability analysis of the groundwater flow showed that the probability of failure from the first and second order reliability method are quite close to that of Monte-Carlo Simulation. from the parametric study of hydraulic conductivity of soil layers, the increase of both mean and variance of hydraulic conductivity results in the increase of probability of exceeding the threshold flow quantity. The probability of failure was more sensitive to constant head located at the end of the flow domain than the other parameters.