Block theory is based on the assumption of the infinite persistence of discontinuities, therefore cannot handle a complex concave shaped block. In practice, it is necessary to consider the persistence of discontinuities to attempt applying the block theory to tunnels. In this paper, a new removability and stability analysis method of rock blocks considering the persistence of discontinuities is proposed as a stability evaluation method in tunnels. Three-dimensional rock block identification considering the persistence of discontinuities is performed by using the discontinuity disc model. The removability and stability analyses of rock blocks formed by the identification method are performed. The new analysis method can handle concave and convex shaped rock blocks. In order to demonstrate the applicability of the new removability and stability analysis method of rock blocks considering the persistence of discontinuities in tunnels, two analysis example problems were carried out. The example problems for convex and concave shaped blocks are presented in this study. The comparison and examinations with the analysis results have confirmed the effectiveness and usefulness of this new removability and stability analysis method of rock blocks considering the persistence of discontinuities proposed as a stability evaluation method in tunnels.