  Abell 2218 is one of a handful of clusters in which X-ray and lensing
analyses of the cluster mass are in strong disagreement. It is also a system
for which X-ray data and radio measurements of the Sunyaev-Zel'dovich decrement
have been combined in an attempt to constrain the Hubble constant. However, in
the absence of reliable information on the temperature structure of the
intracluster gas, most analyses have been carried out under the assumption of
isothermality. We combine X-ray data from the ROSAT PSPC and the ASCA GIS
instruments, enabling us to fit non-isothermal models, and investigate the
impact that this has on the X-ray derived mass and the predicted
Sunyaev-Zel'dovich effect.
  We find that a strongly non-isothermal model for the intracluster gas, which
implies a central cusp in the cluster mass distribution, is consistent with the
available X-ray data and compatible with the lensing results. At r<1 arcmin,
there is strong evidence to suggest that the cluster departs from a simple
relaxed model. We analyse the dynamics of the galaxies and find that the
central galaxy velocity dispersion is too high to allow a physical solution for
the galaxy orbits. The quality of the radio and X-ray data do not at present
allow very restrictive constraints to be placed on H_0. It is apparent that
earlier analyses have under-estimated the uncertainties involved. However,
values greater than 50 km/s/Mpc are preferred when lensing constraints are
taken into account.
