Received date / Accepted date Abstract. We analyse the dust continuum emission seen towards a sample of candidate high-mass protostellar objects, modelling the cores we recently observed at 850 m with a one-dimensional radiative transfer code. Fitting radial slices in a range of directions across sources, we identify a number of objects that have non-spherical density proles and show that for such sources tting the azimuthal averaged emission produces erroneous estimates of the source properties. We nd the majority of cores can be successfully modelled using envelopes of power-law density structure (where / r ), nding a mean power-law index of = 1:3 0:4. These envelopes extend considerably further, are more dense, and have a more shallow density prole than those bearing low-mass protostars. The majority of best-t models have an SED resembling the cold-component dust bodies previously proposed for the sample, implying the short wavelength emission seen towards the HMPOs either originates from a separate hot dust component(s), or involves mechanisms such as accretion disks, stochastic heating and/or optically thin cavities not included in the radiative transfer model. We nd evidence of smaller dust-free cavities towards some pre-UCHII sources. The modelling indicates a correlation between and optical depth, suggesting that the densest cores also tend to have the most strongly peaked power-law density proles.