A system for stress measurement under high pressure has been developed at beamline BL04B1, SPring-8, Japan. A Kawai-type multi-anvil apparatus, SPEED-1500, was used to pressurize polycrystalline KCl to 9.9 GPa in a mechanically anisotropic cell assembly with the KCl sample sandwiched between dense Al2O3 pistons. The variation of deviatoric stress was determined from the lattice distortion measured using two-dimensional X-ray diffraction with monochromatic synchrotron X-rays. The low-pressure B1 phase transformed to the high-pressure polymorph B2 during compression. The deviatoric stress increased with increasing pressure in both the B1 and B2 phases except for the two-phase-coexisting region at a pressure of 2-3 GPa. This new system provides one of the technical foundations for conducting precise rheological measurements at conditions of the Earth's lower mantle.