Strong expansions of products and products in strong shape

The paper is devoted to the study of strong expansions and strong shape of Cartesian products of topological spaces. If the Cartesian product of two spaces X and Y admits a strong expansion, which is the Cartesian product of strong polyhedral expansions of these spaces, then X×Y is a product in the strong shape category. The Cartesian product of two compact Hausdorff spaces is a product in strong shape. The Cartesian product of an FANR with a finitistic space is a product in strong shape.