We present observations of 15 massive cores in three different CS transitions from the FCRAO 14m and the KOSMA 3m telescope. We derive physical parameters of these cores using different approaches to the line radiative transfer problem. The local radiative transfer approximations fail to provide reliable values except for the column densities. A self-consistent explanation of the observed line profiles is only possible when taking density gradients and an internal turbulent structure of the cores into account. The observational data can be fitted by a spherically symmetric radiative transfer model including such gradients and a turbulent clumping. We find that the observed massive cores are approximately virialised with a clumpy density profile that decays with a radial exponent of about -1.6 down to a relatively sharp outer boundary. We show that a careful analysis of spatially unresolved multi-line observations using a physical radiative transfer model can provide values for physical parameters that could be obtained otherwise only by direct observations with much higher spatial resolution. This applies to all quantities directly affecting the line excitation, like the mass and size of dense cores. Information on the exact location or number of clumps, of course, always has to rely on high-resolution observations e.g. from interferometers. Comment: 18 pages, 3 figures, 11 tables, 2 appendices