  We present a strong lens analysis of SDSS J1004+4112, a unique quasar lens
produced by a massive cluster of galaxies at z=0.68, using a newly developed
software for gravitational lensing. We find that our parametric mass model well
reproduces all observations including the positions of quasar images as well as
those of multiply imaged galaxies with measured spectroscopic redshifts, time
delays between quasar images, and the positions of faint central images. The
predicted large total magnification of \mu ~ 70 suggests that the lens system
is indeed a useful site for studying the fine structure of a distant quasar and
its host galaxy. The dark halo component is found to be unimodal centered on
the brightest cluster galaxy and the Chandra X-ray surface brightness profile.
In addition, the orientation of the halo component is quite consistent with
those of the brightest cluster galaxy and member galaxy distribution, implying
that the lensing cluster is a relaxed system. The radial profile of the
best-fit mass model is in good agreement with a mass profile inferred from the
X-ray observation. While the inner radial slope of the dark halo component is
consistent with being -1, a clear dependence of the predicted A-D time delay on
the slope indicates that an additional time delay measurement will improve
constraints on the mass model.
