We develop an analysis method for discontinuous deformation without re-meshing. The proposed method is based on the Finite Cover Method (FCM), which is actually an alias for the Manifold Method. By virtue of the mesh-free nature of the FCM, propagating discontinuous boundaries can be traced regardless of initial mesh discretization. Furthermore, the nonlocal material modeling is introduced to avoid the dependency on mesh size. Representative numerical examples demonstrate the performance of the proposed method and well simulate the propagation of discontinuities with independently generated FCM mesh.