  The aim of this paper is to show that, for any $p \in [1,\infty)$, the
$W^{1,p}$-anisotropic interpolation error estimate holds on quadrilateral
isoparametric elements verifying the maximum angle condition ($MAC$) and the
property of comparable lengths for opposite sides ($clos$), i.e., on all those
quadrilaterals with interior angles uniformly bounded away from $\pi$ and with
both pairs of opposite sides having comparable lengths.
  For rectangular elements our interpolation error estimate agrees with the
usual one whereas for perturbations of rectangles (the most general
quadrilateral elements previously considered as far as we know) our result has
some advantages with respect to the pre-existing ones: the interpolation error
estimate that we proved is written by using two neighboring sides of the
element instead of the sides of the unknown perturbed rectangle and, on the
other hand, conditions $MAC$ and $clos$ are much simpler requirements to verify
and with a clearer geometrical sense than those involved in the definition of
perturbations of a rectangle.
