Nanostructured Cu/304 stainless steel (SS) multilayers were prepared by magnetron sputtering at room temperature. 304SS has a face-centered cubic (fcc) structure in bulk. However, in the Cu/304SS multilayers, the SS layers exhibited fcc structure for layer thickness of less than or equal to 5 nm. For 304SS layer thickness larger than 5nm, bcc 304SS grains were observed to grow on top of the initial ≈ 5 nm of fcc SS. The maximum hardness of Cu/304SS multilayers was ≈ 5.5 GPa (factor of two enhancement compared to rule of mixtures hardness) achieved at a layer thickness of 5nm, with a decrease in hardness with decreasing layer thickness below 5 nm. The hardness of fcc/fcc Cu/304SS multilayers (layer thickness ≤ 5 nm) is compared with Cu/Ni, another fcc/fcc system, to gain insight on how the mismatch in physical properties such as lattice parameters and shear moduli of the constituent layers affect the peak hardness achieved in these nanoscale systems.