Experimental spectra and images of the supernova remnant SN 1006 have been reported for radio, X-ray and TeV gamma-ray bands. Several comparisons between models and observations have been discussed in the literature, showing that the broad-band spectrum from the whole remnant as well as a sharpest radial profile of the X-ray brightness can be both fitted by adopting a model of SN 1006 which strongly depends on the non-linear effects of the accelerated cosmic rays; these models predict post-shock magnetic field (MF) strengths of the order of 150 . Here, we present a new way to compare models and observations, in order to put constraints on the physical parameters and mechanisms governing the remnant. In particular, we show that a simple model based on the classic magnetohydrodynamic (MHD) and cosmic rays acceleration theories (hereafter the ‘classic’ model) allows us to investigate the spatially distributed characteristics of SN 1006 and to put observational constraints on the kinetics and MF. Our method includes modelling and comparison of the azimuthal and radial profiles of the surface brightness in radio, hard X-rays and TeV γ-rays as well as the azimuthal variations of the electron maximum energy. In addition, this simple model also provides good fits to the radio-to-gamma-ray spectrum of SN 1006. We find that our best-fitting model predicts an effective MF strength inside SN 1006 of , in good agreement with the ‘leptonic’ model suggested by the HESS Collaboration. Finally, some difficulties in both the classic and the non-linear models are discussed. Some evidence about non-uniformity of MF around SN 1006 is noted.