  Let $\k$ be an algebraically closed field, let $\A$ be a finite dimensional
$\k$-algebra and let $V$ be a $\A$-module with stable endomorphism ring
isomorphic to $\k$. If $\A$ is self-injective then $V$ has a universal
deformation ring $R(\A,V)$, which is a complete local commutative Noetherian
$\k$-algebra with residue field $\k$. Moreover, if $\Lambda$ is also a
Frobenius $\k$-algebra then $R(\A,V)$ is stable under syzygies. We use these
facts to determine the universal deformation rings of string $\Ar$-modules
whose stable endomorphism ring isomorphic to $\k$, where $\Ar$ is a symmetric
special biserial $\k$-algebra that has quiver with relations depending on the
four parameters $ \bar{r}=(r_0,r_1,r_2,k)$ with $r_0,r_1,r_2\geq 2$ and $k\geq
1$.
