  We consider the following singularly perturbed elliptic problem \[
  - {\varepsilon ^2}\Delta u + u = f(u){\text{ in }}\Omega ,{\text{ }}u >
0{\text{ in }}\Omega ,{\text{ }}u = 0{\text{ on }}\partial \Omega , \] where
$\Omega$ is a domain in ${\mathbb{R}^N}(N \ge 3)$, not necessarily bounded,
with boundary $\partial \Omega \in {C^2}$ and the nonlinearity $f$ is of
critical growth. In this paper, we construct a family of multi-peak solutions
to the equation given above which concentrate around any prescribed finite sets
of local maxima of the distance function from the boundary $\partial \Omega$.
