Summary: A theory is developed for the evolution of bainite as a function of time, temperature, chemical composition and austenite grain size. The model takes into account the details of the mechanism of transformation, including the fact that nucleation begins at the austenite grain surfaces, and that the growth of a sheaf occurs by the repeated nucleation of small platelets. Predictions made using the model are shown to compare well against published isothermal and continuous cooling transformation data.