This study investigated the axial compressive stress dependence of the critical current of Rare Earth Barium-Copper-Oxide (REBCO) double-pancake coils. We measured the critical currents of REBCO coils cooled by liquid nitrogen while various axial compressive stresses from 0 MPa to 130 MPa were applied. After each stress was applied, the critical currents of the coils were also measured without the stress application to examine if the REBCO coils were irreversibly deteriorated. The experimental results showed that the REBCO coils were deteriorated at more than 100 MPa and the critical currents of the coils decreased by about 30% by applying 120 MPa to the coils. Moreover, reversible reduction of the critical currents of the coils were observed while the stresses of less than 100 MPa were applied. The reversible critical current decrease occurred even at a small stress, and the critical currents of the coils were reversibly reduced by about 15% while the stress of 100 MPa was applied. This study quantitatively clarified the dependence of the critical current of the REBCO coil on the axial compressive stress and the limitation of the axial compressive stress to prevent the deterioration of the REBCO coil.