  We consider the following problem: \begin{eqnarray*} ( P)\qquad
\displaystyle\left\{\begin{array} {ll}
  & \Delta^2 u
  = K(x)u^{-\alpha}
  \quad \mbox{ in }\,\Omega , \\ &u> 0\quad \mbox{ in }\,\Omega,
\;\;u\vert_{\partial\Omega}=0, \,\Delta u\vert_{\partial\Omega} = 0.
\end{array}\right.
  \end{eqnarray*} We prove the main existence result:
  Assume that $\alpha+\beta<2$. Then there exists a unique solution $u$ to
$(P)$. Furthermore, there exist $c_1, c_2>0$ such that
\begin{eqnarray}\label{behaviour-bound} c_1 \rho(x)\leq u(x)\leq c_2 \rho(x)
\end{eqnarray}
  where $\rho(x)=d(x,\partial\Omega)$. This result is sharp: Assume that
$\alpha+\beta\geq 2$. Then, there is no solution to $(P)$.
