The ductility of thin metal films on polymer substrates reported in recent experiments has a huge disparity, ranging from less than 1 % up to more than 50 %. To reveal the underpinning origins for such a large variation, this paper reports a systematic computational study of two competing failure mechanisms: metal film necking and grain boundary cracking. The quantitative results suggest that strong grain boundaries and metal/polymer interfacial adhesion are keys to achieve high ductility of polymer-supported metal films.