Abstract: Due to the concealment of the discontinuities, the current exploration technology can not accurately obtain the location and mechanical parameters of all discontinuous, but can only obtain the occurrence information according to the exposure situation. The location of the discontinuities is a key factor for generating a block, so it is necessary to consider all the combinations of the discontinuities and excavation surface, and find the most unfavorable conditions to provide prediction and evaluation for engineering excavation. Based on the construction of joint pyramids, a projection translation method is proposed to solve the maximum movable region for cylindrical excavation surfaces. The dispersing-cutting-assembling method is used to reconstruct the curve surface block. Firstly, a set of radial virtual structures are set up to cut the pyramid block to realize the dispersion of the block. Secondly, based on the classification of face elements, a detailed surface-cutting-element algorithm is proposed. Finally, the cut elements are classified and combined to realize the reconstruction of the curve surface block. A 3D visualization program is developed based on the VC++ and OpenGL. The accuracy, applicability and robustness of the algorithm are verified by a numerical example and an engineering example. The maximum movable block program can be used to select the tunnel direction, providing reference for engineering design.