In REBa2Cu3Oy (RE123, RE=rare earth element) coated conductors, the coexistence of a- and b-axes domains related to a twin structure is one of the origins of the complicated critical current density property and its strain dependence. Hence, control of the twin structure is a very important issue. In the case of Y123 single crystals, detwinning is widely carried out by oxygen annealing under uniaxial stress along the a/b axis. In this study, commercial RE123 superconducting tapes were oxygen-annealed under external strains, similar to the detwinning process of Y123 single crystals. We found that the volume fraction ratio of the a- and b-axis domains changes with the applied external strains during annealing, indicating a change of twin structure. In addition, the residual strains, which are strains induced from the thermal contraction difference between RE123 and the substrate, increase with compression annealing and decrease with tension annealing for RE123 tapes with [100]/[010] orientation along the tape axis. However, those phenomena by strain annealing are not obtained for the [110] oriented RE123 tapes. The strain annealing method that we propose here is very useful to control the internal residual strain and twin structures in an RE123 tape with a [100]/[010] orientation along the tape axis. © 2013 IOP Publishing Ltd.