  In this paper, we focus on studying the distortion of the exterior conformal
modulus of a quadrilateral of sufficiently arbitrary form under the stretching
map along the abscissa axis with coefficient $H\to\infty$. By using the
properties of quasiconformal transformations and taking into account some facts
from the theory of elliptic integrals, we confirm that the asymptotic behavior
of this modulus does not depend on the shape of the boundary of the
quadrilateral. Especially, it is equivalent to $(1/\pi)\log H$ as $H\to\infty$.
Therefore, we give a solution to the Vuorinen problem for the exterior region
of an arbitrary quadrilateral.
