Abstract: In conventional discrete element methods, fracture is judged by criterion of interface and cracks can only propagate along the boundary of elements. However, criterion of interface can only be used rationally on the condition that macro or micro fractures exist in physical problems. The path and direction of crack will be limited severely by the initial mesh when crack propagates along the boundary. Given these two limitations, a continuous-discontinuous element method is proposed and applied to simulate the progressing cracking problem of rocks. Specifically, criterion is applied on element and intra-element fracture will form. In continuous calculation, element is denoted by a discrete spring system which has specific physical meaning and its deformation and stress are calculated by the characteristic length and area of springs in local coordinate system. The continuous calculation results demonstrate a satisfactory agreement with the traditional finite element method. By updating spring information and local coordinate system, large displacement and rotation of elements can be calculated directly. In addition, Mohr-Coulomb criterion is implemented into the new model to specify the failure state and fracture direction, and intact element will be divided into two elements by means of cutting block. In this way, fracture may be inserted along the boundary of elements or within intact element. A cohesive zone model is employed to simulate the fracture and the elements on two sides of the crack are set to two different nodes at the same time, causing the displacement to be discontinuous. Finally, from numerical results of several intense examples with crack propagation, this method can satisfactorily simulate the progressing cracking problems under tensile, compressive and shear conditions, and its rationality is approved. The continuous-discontinuous element method has been shown to be insensitive to quality of mesh and thus has the potential to simulate crack initiation and propagation.