First principle, tight binding, and semi-empirical embedded atom calculations are used to investigate a tetragonal phase transformation in gold nanowires. As wire diameter is decreased, tight binding and modified embedded atom simulations predict a surface-stress-induced phase transformation from a face-centered-cubic (fcc) ⟨100⟩ nanowire into a body-centered-tetragonal (bct) nanowire. In bulk gold, all theoretical approaches predict a local energy minimum at the bct phase, but tight binding and first principle calculations predict elastic instability of the bulk bct phase. The predicted existence of the stable bct phase in the nanowires is thus attributed to constraint from surface stresses. The results demonstrate that surface stresses are theoretically capable of inducing phase transformation and subsequent phase stability in nanometer scale metallic wires under appropriate conditions.