  We study the critical problem {equation} {{array}{ll} \Delta
^{2}u=u^{\frac{N+4}{N-4}} & {in}\Omega\setminus
\bar{B(\xi_0,\varepsilon)},\medskip u>0&{in}\Omega\setminus
\bar{B(\xi_0,\varepsilon)},\medskip u=\Delta u=0 & {on}\partial (\Omega
\setminus \bar{B(\xi_0,\varepsilon)}),{array}. \tag{P$_\varepsilon$} {equation}
where $\Omega$ is an open bounded domain in $\mathbb{R}^N$, $N\ge5$,
$\xi_0\in\Omega$ and $B(\xi_0,\varepsilon)$ is the ball centered at $\xi_0$
with radius $\varepsilon>0$ small enough. We construct solutions of
(P$_\varepsilon$) blowing-up at the center of the hole as the size of the hole
goes to zero.
