Abstract: Flooddischarging tunnel at Jinping First Stage Hydropower Station situates in marbles on right bank of Yalong River where complex geological structures condition appears and the cover depth is more than 100 m. It is clear whether there are key rock blocks on the excavation planes during excavation will sufficiently affect engineering safety. This paper bases on geological conditions in one part of central drift in the flooddischarging tunnel,and draws stochastic probability into key block theory. It studies the generation probability,volume and safety factors of these potential key blocks and obtains the following conclusions. The generation probability of key blocks shows an exponential distribution,on the condition that faults are extended freely. The probability will mainly determined by the length distribution of two joint sets. The relationship between volume of key blocks and trace length of main structural planes is direct ratio. But as trace length increases,the volume of blocks will approach to the maximum value which indicates the complete cut state. The safety factors of key blocks decrease with the growth of the main structuralplane trace length. It has a minimum value which shows the complete cut state. These are useful to offer effective reinforcement design and have important engineering values.