We use nonlinear kinetic theory of cosmic ray acceleration in supernova remnants to study the properties of the nonthermal emission from SN 1006. The range of physical parameters is examined in order to find out whether it encompasses the existing data. It is shown that the gamma-ray flux is very sensitive to the ambient gas density NH and that the existing H.E.S.S. upper limit requires NH ≦ 0.1 cm–3