Young’s moduli of superelastic NiTi wires in austenite and stress-induced martensite states were evaluated by three different experimental methods (tensile tests, in situ synchrotron x-ray diffraction, and dynamic mechanical analysis) and estimated via theoretical calculation from elastic constants. The unusually low value of the Young’s modulus of the martensite phase appearing in material property tables (<40 GPa) is generally ascribed in the literature to the fact that stress-driven martensitic transformation and/or twinning processes continue even beyond the transformation range and effectively decrease the value of the tangent modulus evaluated from macroscopic stress-strain curve. In this work, we claim that this low value is real in the sense that it corresponds to the appropriate combination of elastic constants of the B19′ martensite phase forming the polycrystalline wire. However, the Young’s modulus of the martensite phase is low only for wire loaded in tension, not for compression or other deformation modes. It is shown that the low value of the martensite Young’s modulus in tension is due to the combination of the unique coincidence of elastic anisotropy of the B19′ martensite characterized by the low elastic constant C55, austenite drawing texture, and strong martensite texture due to the martensite variant selection under tensile stress.