  The thickness of a graph $G$ is the minimum number of planar subgraphs whose
union is $G$. In this paper, we present sharp lower and upper bounds for the
thickness of the Kronecker product $G\times H$ of two graphs $G$ and $H$. We
also give the exact thickness numbers for the Kronecker product graphs
$K_n\times K_2$, $K_{m,n}\times K_2$ and $K_{n,n,n}\times K_2$.
