ABSTRACT: The classical block theory concentrates on the convex blocks. Most traditional methods or algorithms only accept convex combination of free planes and produce convex key block, especially the block modeling methods. However, non-convex cases are also common in practical engineering projects, e.g., the non-convex key block at the edges, corners or portals of the underground chambers. Based on the key block identification methods from classical block theory and the theory of Nef polyhedra, non-convex key block modeling methods are proposed in this paper. Once the composition of the joint and free planes is determined for the non-convex key block, the shape of the block can be generated via the 3D boolean operations on either the convex sub-blocks or the half-spaces defined by all the planes. Experimental results show that the proposed methods can generate non-convex key blocks from complex combination of joint and free planes accurately and efficiently.