The movement of dislocations, under the potential energy and the external driving forces, affects the performance of materials in various applications. This paper demonstrates meshless Dynamic Relaxation (DR) technique and the Embedded Atom method (EAM) potential function for simulations of the relaxation of atomistic models with dislocation defects subjected to external forces. A newly developed periodic symmetry method is incorporated into the algorithm and applied to one coordinate direction of the atomistic model, as well as the net traction on the periodic boundary in order to mimic an infinite bulk with a finite number of atoms. Output stress and displacement components are used to visualize the results and are in agreement with theoretical analysis. The numerical treatments, such as the application of the new periodic symmetry technique in the EAM potential model, the convergence criterion, the unit length, the choice of damping ratios in different cases and the stable range of net traction, are studied. The example case, which illustrates the pure edge dislocation model with and without the external force along the periodic direction, is successfully implemented and presented in the paper.