The cystallographic texture and elastic constants have been measured on heat-treated Zr-2.5%Nb alloy pressure tubes by neutron diffraction. The texture of heat-treated Zr-2.5%Nb alloy is not so strongly oriented compared with that of non-heat-treated Zr-Nb alloy. However, the pole figures show that the appropriate diffraction planes for the axial direction strain are 10·0, 00·2 or 10·1 diffractions, those for the hoop direction strain are 00·2, 10·1 or 11·0 diffractions, and those for the radial direction strain are 11·0 or 10·2 diffractions. The diffraction plane dependency of elastic constants almost agrees with that obtained from Kröner's single cristal model. However, the diffracttion plane dependency of elastic constants is not so strong. From the residual stress measurements by the neutron diffraction, the values of Young's modulus for 10·0, 10·1 and 00·2 diffractions are found to be 96GPa, 95GPa and 104GPa, respectively, and Poisson's ratios are 0.34, 0.36 and 0.32, respectively. Finally, the residual stress evaluation method for the material with strongly oriented texture is proposed.