Cable-stayed bridges are landmark structures and key parts of transportation networks worldwide. It is of vital importance that their integrity is ensured even under very large earthquakes. The spatial variability of the ground motion could be a significant aspect of the seismic behaviour of long-span cable-stayed bridges due to the differential movement of the pylons, which may lead to an amplified seismic response and increased damage in the pylons. The purpose of this paper is to examine the effect of the spatial variability of the ground motion on the seismic response of cable-stayed bridges with H-shaped pylons and various span lengths. Focus is placed on the pylons of the bridges because the constitute key members for the overall stability and structural integrity of the bridge. The study explores how important the spatial variability is in the seismic response of cable-stayed bridges by considering two different orientations of the structures with respect to the seismic fault in an extensive program of non-linear response-history analyses.