We present calculations of the radio images and light curves from supernovae, based on high-resolution numerical simulations of the hydrodynamics and radiation transfer in a spherically symmetric medium. As a specific example we model the emission from SN1993J. This supernova does not appear to be expanding in a self-similar fashion, and cannot be adequately fitted with the often-used analytic mini-shell model. We present a good fit to the radio evolution at a single frequency. Both free-free absorption and synchrotron self-absorption are needed to fit the light curve at early times, and a circumstellar density profile of ρ ~ r−1.7 provides the best fit to the later data. Comparisons of VLBI images of SN1993J with synthetic model images suggest that internal free-free absorption completely obscures emission at 8.4 GHz passing through the center of the supernova for the first few tens of years after explosion.