  Let $G$ be a finite simple graph on $n$ vertices. Let $J_G \subset K[x_1,
\ldots, x_n]$ be the cover ideal of $G$. In this article, we obtain syzygies,
Betti numbers and Castelnuovo-Mumford regularity of $J_G^s$ for all $s \geq 1$
for certain classes of graphs $G$.
