Understanding the characteristic response of critical current, I c with stress/strain under magnetic field is important for the application of coated conductor (CC) tapes to large scale superconducting coils or magnets. In this study, the strain and magnetic field effects on I c in brass laminated reactive co-evaporation by deposition and reaction (RCE-DR) processed GdBCO CC tapes at 77 K were investigated. In the case of RCE-DR GdBCO CC tape samples with Hastelloy substrate, the additional lamination of brass foils to the Cu-stabilized only resulted in an increased irreversible strain limit of 0.50 % up to 0.80 %. But, not as much of these improvements were observed in CC samples having stainless steel substrate. Also, the additional brass laminate to all GdBCO CC tape samples did not affect the magnetic field response of Ic at 0 % strain. Under magnetic field, the strain response and tolerance of Ic was improved with additional brass laminates showing a much lower Ic reduction as compared with that at the irreversible strain limit of the Cu-stabilized CC samples. The strain sensitivity behavior of Ic under magnetic field (I c-ε-B relation at 77 K) in RCE-DR GdBCO CC tapes was discussed.