To take the advantages of both the FEM and the particle DEM methods, a procedure is proposed to transit the FEM into the DEM. In this procedure, the domain of concern is first discretized into a certain number of coarse FEM elements, and the behavior of each element is characterized by using a continuum constitutive model. During simulation, the stress state of each element is tracked for each time step. Once if the stress state of an element satisfies either the Mohr-Coulomb criteria or the maximum tensile stress criteria, the element is deleted and immediately replaced by a cluster of particles, which are randomly distributed and slightly interpenetrated. As such, the response of the deleted element is fully described by this cluster of particles. The particle properties of the cluster, including mass, material properties, velocity, displacement and contact force, are all inherited from the deleted element by using an interpolation method. To realize the simulation coupling FEM and particle DEM, the point-edge (2D) and point-face (3D) contact models are introduced, and the contact forces are calculated using normal and tangent numerical springs. Numerical examples such as the impact of a particle ball onto a slab, the uniaxial compression and rock cutting, are provided to illustrate the capability of the proposed method.