Random blocks in underground tunnels and in grand power caverns are the unstable blocks cut by random joints or fractures in the bedrock. Designers often reinforce these blocks by using systematic anchors however their length and space are difficult to determine because of the randomness of blocks position and the indeterminacy of the blocks geometric characters. By the study of geological conditions and the rock structure of the underground caverns in the hydropower station, the regularities of distribution of the possible random joints were concluded. This enabled the random blocks to be orientated by combining joints with other joints, or combining joints with I and II definite structural planes. The geometric characteristics and stabilities of the random blocks were determined by using stability calculations according to block theory. From this the optimal anchor length could be defined, which could be referred to as a theoretical base for the length of the systematic anchors.published_or_final_versionThe 10th IAEG International Congress: Engineering Geology for Tomorrow's Cities, Nottingham, United Kingdom, 6-10 September 2006. In Proceedings of the 10th IAEG International Congress, 2006, p. 547-55