The structural characterization of the orientation and elongation under shear flow in Lyotropic Chromonic Liquid Crystals (LCLCs) molecules, Sunset Yellow FCF (SSY), was performed by in situ rheological small/wide angle X-ray scattering (Rheo-SAXS/WAXS). The X-ray measurement results clearly demonstrated that the stacked aggregates were oriented and elongated to the shear direction under shear flow. Further shear rate increase caused the enhancement in the orientation and elongation with the inter-aggregate distance constant, and then the structural change decreased implying the onset of the orientation saturation at high shear rates.