Part 1 examines the behavior of the solution of (1) \(-\Delta u+g(u)=f\) in \(\Omega \setminus \{0\}\subset\mathbb R^ 2\) near 0, where \(g\in C(\mathbb R)\) is assumed to be non-decreasing and \(f\in C^ 0(\Omega)\). It is shown that (i) if \(| g|\) has ``super-exponential'' growth (for \(| r| \to \infty)\) the isolated singularity at 0 is removable; this means \(u\) has a \(C^ 1(\Omega)\)-extension which solves (1) in \(\Omega\)); (ii) if \(g\) is truly of exponential type, then \(u\) has a weak (logarithmic) singularity; (iii) if \(g\) is of polynomial type \(u\) may have a weak or strong singularity at 0. Part 2 shows that the solution of (2) \(-\Delta u+g(\cdot,u)=0\) in \(\Omega \setminus \Sigma \subset\mathbb R^ n\) \((n>2)\) has a \(C^ 1(\Omega)\)-extension which solves (2) in \(\Omega\) (this means \(\Sigma\) is a removable singularity) if (iv) \(\Sigma\) is a \(C^ 1\) compact submanifold of \(\Omega\) of dimension \(n-2\); (v) \(g(x,r)\) is continuous and has ``super-exponential'' growth for \(| r| \to \infty\) uniformly on \(\Omega\).