In this paper we analyze the blow-up rates of large solutions to the semilinear elliptic problem $\Delta u =b(x)f(u), x\in \Omega, u|_{\partial \Omega} = +\infty,$ where $\Omega$ is a bounded domain with smooth boundary in $R^N$, $f$ is rapidly varying or normalised regularly varying with index $p$ ($p>1$) at infinity, and $b \in C^\alpha (\bar{\Omega})$ which is non-negative in $\Omega$ and positive near the boundary and may be vanishing on the boundary.