  Associated to a symmetrisable Cartan matrix $C$, Geiss-Lerclerc-Schr\"{o}er
constructed and studied a class of Iwanaga-Gorenstein algebras $H$. They proved
a generalised version of Gabriel's Theorem, that is, the rank vectors of
$\tau$-locally free $H$-modules are the positive roots of type $C$ when $C$ is
of finite type, and conjectured that this is true for any $C$. In this paper,
we look into this conjecture when $C$ is of affine type. We construct
explicitly stable tubes, some of which have rigid mouth modules, while others
not. We deduce that any positive root of type $C$ is the rank vector of some
$\tau$-locally free $H$-module. However, the converse is not true in general.
Our construction shows that there are $\tau$-locally free $H$-modules whose
rank vectors are not roots, when $C$ is of type $\widetilde{\mathbb{B}}_n$,
$\widetilde{\mathbb{CD}}_n$, $\widetilde{\mathbb{F}}_{41}$ and
$\widetilde{\mathbb{G}}_{21}$, and so the conjecture fails in these four types.
