Let (M, g) be a compact Riemannian manifold of dimension \(n \geq3\). In this paper, we define and introduce the prescribed scalar curvature problem with singularities. Under some assumptions, we show that there exists a conformal metric \(\overline{g}\) such that its scalar curvature \(S_{\overline{g}}\) equals some given function. This problem is equivalent to studying the existence and regularity of the solution to what we will call the singular prescribed scalar curvature equation.