  The paper is devoted to the study of coarse shape of Cartesian products of
topological spaces. If the Cartesian product of two spaces $X$ and $Y$ admits
an HPol-expansion, which is the Cartesian product of HPol-expansions of these
spaces, then $X\times Y$ is a product in the coarse shape category. As a
consequence, the Cartesian product of two compact Hausdorff spaces is a product
in the coarse shape category. Finally, we show that the shape groups and the
coarse shape groups commute with products under some conditions.
