Peridynamics is a non-local theory proposed for the effective handling of discontinuities such as propagation, branching, and coalescing of cracks. Collective information of the displacements of peridynamic particles is used to calculate the deformation gradient, and the equation of the motion is naturally integrodifferential. Using the integrodifferential equations, peridynamics can describe the discontinuities without additional criteria, while the classical continuum mechanics, finite element method (FEM), requires the conditions to predict the discontinuities. However, the computational efficiency of peridynamics is expensive compared to FEM because peridynamics calculates stress fields using the collective information of the displacements of the neighboring particles within the certain distance of the target particle, while FEM limits the interaction to adjacent nodes in the element. Therefore, coupling peridynamics and FEM provides both advantages of peridynamics in solving the discontinuities without additional criteria as well as the high computational efficiency of FEM.