We have investigated the relationship between perpendicular magnetic anisotropy (PMA) and the magnetoelastic effect of Co/Rh(111) epitaxial superlattices as a large mismatch system and found the PMA for the thin Co layer to be less than 12 Angstrom. The magnitude of the PMA is comparable to those of typical PMA systems such as Co/Pd and Co/Pt. By taking account of the Co-thickness-dependent magnetoelastic anisotropy K-ME, arising from the lattice strain due to the 7% mismatch between Co and Rh, we found that the thickness-dependent PMA can be reproduced with no adjustable parameter. (C) 2005 American Institute of Physics.