  The ternary uranium compound UCu$_2$Sn with a hexagonal ZrPt$_2$Al-type
structure shows a phase transition at 16 K. We reported previously that huge
lattice-softening is accompanied by the phase transition, which originates from
ferroquadrupolar ordering of the ground state non-Kramers doublet $\Gamma_5$. A
macroscopic strain, which is expected to emerge spontaneously, was not detected
by powder X-ray diffraction in the temperature range between 4.2 and 300 K. To
search the spontaneous strain, we have carried out thermal expansion
measurements on a single-crystalline sample along the $a$, $b$ and $c$ axes
using a capacitance technique with the resolution of $10^{-8}$. In the present
experiment, we found the spontaneous $e_{xx} - e_{yy}$ strain which couples to
the ground state doublet $\Gamma_5$. The effect of uniaxial pressure along the
$a$, $b$ and $c$ axes on the transition temperature is also discussed.
