Finite element (FE) simulations were performed to study yielding in single and bilayer (BL) film systems using a “yield zone map” approach. Onset of yielding was observed at the interface, substrate, surface, and film in HfB2/silicon and HfB2/stainless steel systems. The interface yield zone in HfB2/stainless steel system was found to be larger due to the dominant effect of interfacial stress gradients. Based on the FE simulations, empirical equations were derived for the maximum contact pressure required to initiate yield at the interface. For BL/substrate systems, onset of yield at the lower film/substrate interface occurred when film thickness ratio was in the range 0.5–5. The maximum contact pressure associated with the initial yielding at this interface is minimum compared to other locations. From the design point of view, for a BL system the preferable film thickness ratio was found to be 20, whereas the optimum hardness ratio ranges from 2 to 4. For these values, maximum contact pressure is very high (∼30 GPa), and thus, yield onset can be avoided at lower film/substrate interfaces. In addition, based on the obtained results, the advantages and disadvantages of using a BL film as compared to a single film and their relevance to practical applications are discussed.