We report a systematic simulated annealing study of the energetics of bi-layer height steps with edges running parallel (A type), perpendicular (B type) and at 45° (C type) to surface As dangling orbitals on As(2 × 4) reconstructed GaAs(001) vicinal surfaces. Employing semi-empirical interatomic potentials having two- and three-body interaction terms, we calculate the step energy and the step-step interaction energy as a function of the step separation. The step-step interaction energies are attractive for B type steps and repulsive for A and C types, in all cases decreasing in magnitude with increasing step separation. The results affirm a connection between the orientation of dangling orbitals at the step edge and the corresponding step-step elastic interaction induced nature and directionality of the surface stress. Such surface stress could be a driving force for the directional migration of atoms observed in the case of MBE growth on patterned non-planar GaAs substrates that has led to the realization of quantum wire and quantum box structures.