The 'developmental stress hypothesis' attempts to provide a functional explanation of the evolutionary maintenance of song learning in songbirds. It argues that song learning can be viewed as an indicator mechanism that allows females to use learned features of song as a window on a male's early development, a potentially stressful period that may have long-term phenotypic effects. In this paper we formally model this hypothesis for the first time, presenting a population genetic model that takes into account both the evolution of genetic learning preferences and cultural transmission of song. The models demonstrate that a preference for song types that reveal developmental stress can evolve in a population, and that cultural transmission of these song types can be stable, lending more support to the hypothesis.