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High energy X-ray synchrotron diffraction is used to investigate the elastic anisotropy of the nickel-based superalloy IN718 produced by laser powder bed fusion (PBF-LB). This material is characterized by a columnar grain morphology with some crystallographic texture. The material is subjected to elastic loading to determine the diffraction elastic constants (DECs). Furthermore, the single-crystal elastic constants (SCEC) are refined from these experiments using different micromechanical models. The results show that each micromechanical model predicts a specific set of SCEC that well describes the elastic anisotropy of PBF-LB/IN718.