The tensile strain dependences of the critical current (I-c) in YBa2Cu3O7-delta (YBCO) coated conductors fabricated by using the rolling-assisted biaxially textured Ni-W substrates (RABiTS)-pulsed laser deposition (PLD) method were examined at 77 K and in self magnetic field. Cu and stainless steel layers were used as stabilizers to the YBCO coated conductor, and the effects of stabilizing layers on the strain tolerance of I-c were investigated, compared with the case without a stabilizing layer. The lamination of stabilizer produced an increase in the yield strength and strain tolerance of I-c in coated conductors. All YBCO coated conductors tested showed a reversible strain effect and a peak in the relation between I-c and applied strain. The peak strain of I-c and the irreversible strains for I-c degradation were enhanced when the YBCO coated conductor was laminated with a stabilizing layer. For the case laminated with a stainless steel layer, I-c recovered reversibly until the applied strain reached to about 0.5% and showed its peak at a strain of 0.42%, comparing to the case without a stabilizing layer, which were 0.21% and 0.18%, respectively. It can be predicted that the lamination of a stabilizing layer produced a significant residual compressive strain to the YBCO film during cooling to 77 K, which influenced the axial strain tolerance of YBCO coated conductors. Therefore, the I-c-tensile strain relation in YBCO coated conductors could be explained by a two-stage deformation; stage I is the region where YBCO film behaves elastically and I-c recovers when the stress is released. Stage 11 is the region where I-c decreases irreversibly attributable to the cracking induced in the YBCO film due to the significant plastic deformation of the substrate or the stabilizing layer.