  Let $G$ be a simple graph of order $n$. The domination polynomial of $G$ is
the polynomial $D(G, x)=\sum_{i=\gamma(G)}^{n} d(G,i) x^{i}$, where $d(G,i)$ is
the number of dominating sets of $G$ of size $i$ and $\gamma(G)$ is the
domination number of $G$. In this paper we consider cactus chains with
triangular and square blocks and study their domination polynomials.
