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SmBCO and YBCO coated conductors (CC) showed different critical current, Ic degradation behavior with strain showing different Ic peak position under self field. Strain effect on Ic under magnetic field in REBCO CC tapes was investigated in order to measure and to describe its tolerance and degradation behavior. Katagiri-type tensile testing apparatus was adopted in which magnetic field was applied parallel to the c-axis of coating film using 10 T superconducting magnet at 77 K. Both strain gauge and Nyilas double extensometers were used to measure the strain. In all the REBCO CC tapes investigated, Ic(ε, B) strongly depends on magnetic field and their degradation behavior depends on the kind of HTS film and fabrication technique adopted. Differently with YBCO CC tapes, SmBCO CC tapes showed increasing Ic strain sensitivity with increasing magnetic field at 77 K and the irreversible strain limit was magnetic field independent over the entire field range studied.