We show that if $\G$ is a finitely presented metabelian group, then the ``untwisted" fibre product or pull-back $P$ associated to any short exact sequence $1\to N\to \G\to Q\to 1$ is again finitely presented. In contrast, if $N$ and $Q$ are abelian, then the analogous ``twisted" fibre-product is not finitely presented unless $\G$ is polycyclic. Also a number of examples are constructed, including a non-finitely presented metabelian group $P$ with $H_2(P,\Z)$ finitely generated.