We present a model for the non-thermal emission from the historical supernova remnant SN 1006. We constrain the synchrotron parameters of the model with archival radio and hard X-ray data. Our stationary emission model includes two populations of electrons, which is justified by multifrequency images of the object. From the set of parameters that predict the correct synchrotron flux we select those which are able to account, either partly or entirely, for the gamma-ray emission of the source as seen by HESS. We use the results from this model as well as the latest constraints imposed by the Fermi observatory and conclude that the TeV emission cannot be accounted for by π0 decay from high-energy ions with a single power-law distribution, of the form , and s ≳ 2.