  A mass model of the rich cluster A2218 is presented based on optical and new
near-infrared images of arc(let)s and the ROSAT/HRI X-ray map. A lensing model
is proposed with two dark matter clumps, centered on the two bright galaxies
around which the various arcs are observed. Two of them, close to the most
massive clump around the brightest galaxy, are required to be fold images,
given their position angle with respect to the major axis. A third image for
each of the two arcs is then predicted to be on the opposite side of the major
axis. Both images are indeed found at the expected positions, with consistent
magnitudes, colors and shapes. One of the arcs has a known redshift of $0.7$,
and the model predicts that the other arc should be at higher redshift, $z
\approx 3$. Photometric data in UBrzJK' indicates that a redshift close to 3 is
indeed probable for this arc. The dark matter halo is found to be sharply
peaked on the giant central galaxy. The ROSAT/HRI X-ray map shows a strongly
clumped image, poorly correlated with the cD light and the mass model on scales
below $\sim$ 200$h_{50}^{-1}$kpc, but similar to the distribution of galaxies
and the mass model when smoothed on this scale. The large degree of central
substructure implied helps to account for the discrepancy previously found (in
the two massive clusters A2218 \& A1689) between the mass derived from the
gravitational lenses and that derived from the X-ray profile and temperature
distributions, in a model of hydrostatic equilibrium. Most of the discrepancy
can probably be explained by bulk motions and acceleration of the gas, and
projection effects enhancing the lensing power of the cluster.
