An upgrading of the 25 T cryogen-free superconducting magnet (CSM) at the HFLSM to a 30T-class CSM is considered by replacing the present Bi2223 insert coil with a REBCO ones, since REBCO tapes have better mechanical and in-field critical current properties. In our strategy for the REBCO coil of the 30T-CSM, two tapes co-winding technique will be adopted in order to increase the space current density in the coil and to avoid a hotspot generation due to local degradation. Electromagnetic and mechanical properties of two bundle co-wound (two-ply) pancake coils are investigated as an R&D test coil for the 30T-CSM. The R&D coils were fabricated with Fujikura REBCO tapes that have 4.1 mm width and 0.11 or 0.15 mm thickness depending on the coil. The coil voltages and strains were measured at 4.2 K under a background field of 11 T. The maximum hoop stress up to 460-530 MPa at the outermost winding estimated by the BJR relation was applied, and no degradation by the hoop stress was found.