  Let $R$ be a finite valuation ring of order $q^r.$ Using a point-plane
incidence estimate in $R^3$, we obtain sum-product type estimates for subsets
of $R$. In particular, we prove that for $A\subset R$, $$|AA+A|\gg
\min\left\{q^{r}, \frac{|A|^3}{q^{2r-1}}\right\}.$$ We also show that if
$|A+A||A|^{2}>q^{3r-1}$, then $$|A^2+A^2||A+A|\gg
q^{\frac{r}{2}}|A|^{\frac{3}{2}}.$$
