Let be a graph. The distance between the vertices and of the graph is equal to the length of a shortest path that connects and . The Wiener index is the sum of all distances between vertices of , whereas the hyper-Wiener index is defined as . In this paper the hyper-Wiener indices of the Cartesian product, composition, join and disjunction of graphs are computed. We apply some of our results to compute the hyper-Wiener index of nanotubes, nanotori and -multi-walled polyhex nanotori.