  We study a general elliptical potential of the form $\psi(x^2+y^2/q^2)~
(0<q\le 1)$ plus an additional shear (with an arbitrary direction) as models
for the observed quadruple lenses. It is shown that a minimum additional shear
is needed even just to reproduce the observed positions alone. We also obtain
the dependence of the axial ratio, $q$, on the orientation of the major axis of
potential. A general relation also exists between the shear, the position angle
and axial ratio of the lensing galaxy. The relation shows a generic degeneracy
in modelling quadruple lenses. In particular, it shows that only the ratio of
the ellipticity, $\epsilon\equiv (1-q^2)/(1+q^2)$, to the magnitude of shear,
$\gamma$ can be determined. All these results are valid regardless of the
radial profile of the potential. Our formalism applies when the galaxy position
is observed, which is the case for seven of the eight known quadruple lenses.
Application to these seven cases reveals two quadruple lenses CLASS 1608+656
and HST 12531-2914, requiring highly significant shear with magnitude $\approx
0.2$. For HST 12531-2914, there must be a misalignment between the major axis
of light and the major axis of potential (mass). We conclude that detailed
modelling of quadruple lenses can yield valuable quantitative information about
the shape of lensing galaxies and their dark matter halos.
