This thesis presents an approach for implementing a Peridynamic technique on a Graphics Processing Unit (GPU). The Peridynamic theory is a non local theory in continuum mechanic, with a focus on discontinuous functions as they arrive in fracture mechanics. The word Peridynamic is the syncrisis of the two Greek words peri = near and dynami = force. The principle of this theory is, that particles in a continuum interact with other particles in a finite distance by exchanging forces. For the implementation on the GPU the Compute Unified Device Architecture (CUDA) is used.