In seeking to understand at a microscopic level the response of dislocations to stress we have undertaken to study as completely as possible the simplest case: a single dislocation in a two dimensional crystal. The intention is that results from this study will be used as input parameters in larger length scale simulations involving many defects. We present atomistic simulations of defect motion in a two-dimensional material consisting of atoms interacting through a modified Lennard-Jones potential. We focus on the regime where the shear stress is smaller than its critical value, where there is a finite energy barrier for the dislocation to hop one lattice spacing. In this regime motion of the dislocation will occur as single hops through thermal activation over the barrier. Accurate knowledge of the barrier height is crucial for obtaining the rates of such processes. We have calculated the energy barrier as a function of two components of the stress tensor in a small system, and have obtained good fits to a functional form with only a few adjustable parameters.