<p>The classical continuum mechanics fails in case of discontinuities. Peridynamics has been proven to be a powerful tool for solving such problems. However, it is extremely computational expensive and there are difficulties in fulfilling local boundary conditions. The paper aims to overcome these problems by coupling the Peridynamics (PD) with the Finite Element Method (FEM). Three different coupling strategies are considered in the paper: modified Schwarz Alternating Method, the Arlequin based coupling method and the Splice Method. The methods are presented and applied to one-dimensional dynamic cases, including high-frequency wave propagation analysis. The criteria applied to evaluate the methods are convergence to the local solution and difficulties choosing specific numerical parameters. The significance of long-range forces in the nature of the damage is also examined.</p>