We have developed a detailed stellar evolution code capable of following the simultaneous evolution of both stars in a binary system, together with their orbital properties. To demonstrate the capabilities of the code we investigate potential progenitors for the Type IIb supernova 1993J, which is believed to have been an interacting binary system prior to its primary exploding. We use our detailed binary stellar evolution code to model this system to determine the possible range of primary and secondary masses that could have produced the observed characteristics of this system, with particular reference to the secondary. Using the luminosities and temperatures for both stars (as determined by Maund et al. 2004) and the remaining mass of the hydrogen envelope of the primary at the time of explosion, we find that if mass transfer is 100 per cent efficient the observations can be reproduced by a system consisting of a 15 solar mass primary and a 14 solar mass secondary in an orbit with an initial period of 2100 days. With a mass transfer efficiency of 50 per cent, a more massive system consisting of a 17 solar mass primary and a 16 solar mass secondary in an initial orbit of 2360 days is needed. We also investigate some of the uncertainties in the evolution, including the effects of tidal interaction, convective overshooting and thermohaline mixing.