The movement and interactions of dislocations, under the potential energy and the external driving forces, affect the performance of materials in various applications. The Dynamic Relaxation (DR) technique, the Embedded Atom method (EAM) potential function and a newly developed periodic symmetry method are combined and expanded for simulations of the relaxation of atomistic models with dislocation defects subjected to two-dimensional external forces. This paper focuses on solving two challenges in the simulation: (i) it evaluates correct internal forces and corresponding external forces with more complicated periodic boundary in the model and (ii) finds a proper way to revise the displacement field of atoms in the boundary layers to satisfy the requirements of the periodic symmetry in the direction other than the direction of dislocation line. The numerical parameters, such as the choice of damping ratios and the variation of forces in different directions, are studied. The example given, illustrated by behaviour of stress and/or displacement components, deals with and compares the relaxation of a dislocation model under biaxial external forces.