The Fe3Al alloy with D03 structure exhibits large recoverable strains due to reversible slips. Tension and compression experiments were conducted on single crystals of Fe3Al, and the onset of slip in forward and reverse directions were obtained utilizing high-resolution digital image correlation technique. The back stress provides the driving force for reversal of deformation upon unloading, resulting in a superelastic phenomenon as in shape memory alloys. Using density functional theory simulations, we obtain the energy barriers (GSFE – generalized stacking fault energy) for {1 1 0}〈1 1 1〉 and {1 1 2}〈1 1 1〉 slips in D03 Fe3Al and the elastic moduli tensor, and undertake anisotropic continuum calculations to obtain the back stress and the frictional stress responsible for reversible slip. We compare the theoretically obtained slip stress magnitudes (friction and back stress) with the experimental measurements disclosing excellent agreement.