ABSTRACT: The focus of classical block theory is convex block, such as in the wall or roof of underground caverns. However, there may exist non-convex key blocks in the edges, corners, portals of underground caverns and even in the corners of crossed tunnels. If a nonconvex block is viewed as a combination of several convex blocks, the identification criteria for finiteness and removability of non-convex block can be created. On the basis, the algorithm that a non-convex block can be cut into several convex blocks along some of the free planes is proposed. And the identification of the complex blocks is achieved. Experimental results show that the algorithm can solve many block identification problems under the conditions of various complex engineering structures.