Abstract: Random blocks in underground tunnels are those uncertain blocks cut by random joints or fractures in bedrock, which have been observed in many existing underground factory buildings. Designers often reinforce these blocks by using systematic anchors, of which length and space are difficult to determine because of the randomness of the blocks position and the indeterminacy of the blocks geometry. This paper presents a case study in a hydropower station to demonstrate distribution patterns of the random joints based on geological conditions and rock structure of the underground caverns. Potential random blocks are then defined by combining different sets of joints, or by combining joints with the Type I and II structural planes. Stabilities of the random blocks are eventually evaluated using the block theory. Finally, the optimal anchor length can be determined as part of the design of the systematic anchors.