The stress/strain dependence of elastic property of the surround Cu stabilized YBCO coated conductor was precisely investigated by means of white X-ray and pulsed neutrons. Multiple diffraction peaks were observed along axial and lateral directions with the tape axis as a function of tensile load. The following unusual stress/strain behaviors exerted on the YBCO layer were made clear. Pairs of (020)/(200) and (040)/(400) were observed side by side in two rows and their diffraction intensity was almost constant with increasing tensile load. The ratio of diffraction strain to external strain became less than unity. The diffraction elastic constants estimated from (0k0) diffraction peaks were larger than from (h00) peaks. Their observations strongly suggest that the micro twin structure is key nanostructure to understand the microscopic elastic constant and strain obtained from the diffraction experiments.