  Fifty-one dense cores associated with water masers were mapped at 350 micron.
These cores are very luminous, 10^3 < Lbol/Lsun < 10^6, indicative of the
formation of massive stars. Dust continuum contour maps and photometry are
presented for these sources. The spectral energy distributions and normalized
radial profiles of dust continuum emission were modeled for 31 sources using a
one-dimensional dust radiative transfer code, assuming a power law density
distribution in the envelope, n = n_f (r/r_f)^{-p}. The best fit density power
law exponent, p, ranged from 0.75 to 2.5 with <p> = 1.8 +/- 0.4. The mean value
of p is comparable to that found in regions forming only low mass stars. The
mean p is incompatible with a logatropic sphere (p = 1), but other star
formation models cannot be ruled out. Different mass estimates are compared and
mean masses of gas and dust are reported within a half-power radius determined
from the dust emission and within a radius where the total density exceeds 10^4
cm^3. Evolutionary indicators commonly used for low mass star formation may
have some utility for regions forming massive stars. For comparison with
extragalactic star formation studies, the luminosity to dust mass ratio is
calculated for these sources with a method most parallel to that used in
studies of distant galaxies and is found to be similar to that seen in high
redshift starburst galaxies.
