  In this paper, we consider the following critical polyharmonic equation
\begin{align*}%\label{abs} ( -\Delta)^m u+V(|y'|,y'')u=u^{m^*-1},\quad u>0,
\quad y=(y',y'')\in \mathbb{R}^3\times \mathbb{R}^{N-3},
  \end{align*} where $m^*=\frac{2N}{N-2m}$, $N>4m+1$, $m\in \mathbb{N}^+$, and
$V(|y'|,y'')$ is a bounded nonnegative function in $\mathbb{R}^+\times
\mathbb{R}^{N-3}$. By using the reduction argument and local Poho\u{z}aev
identities, we prove that if $r^{2m}V(r,y'')$ has a stable critical point
$(r_0,y_0'')$ with $r_0>0$ and $V(r_0,y_0'')>0$, then the above problem has a
new type of solutions, which concentrate at points lying on the top and the
bottom circles of a cylinder.
