The edge-bandwidth of a graph G is the smallest number for which there is a bijective labeling of with such that the difference between the labels at any adjacent edges is at most . Here we compute the edge-bandwidth for rectangular grids:where is the Cartesian product and denotes the path on n vertices. This settles a conjecture of Calamoneri et al. [New results on edge-bandwidth, Theoret. Comput. Sci. 307 (2003) 503–513]. We also compute the edge-bandwidth of any torus (a product of two cycles) within an additive error of 5.