In this paper, we are devoted to studying the positive weak, punctured or distributional solutions to the biharmonic Lane–Emden equation \(\begin{aligned} \Delta ^{2} u=u^{p} \quad \quad \text {in} \ \mathbb {R}^{N}\setminus Z, \end{aligned}\) where \(N\ge 5\) , \(1<p\le \frac{N+4}{N-4}\) , and the singular set Z represents a closed and proper subset of \( \left\{ x_{1}=0\right\} \) . The symmetry and monotonicity properties of the singular solutions will be given by taking advantage of the moving plane method and the approach of moving spheres.
