This paper presents a three-dimensional dynamic response of a structure with a rigid footing to a two-dimensional alluvial valley which is subjected to non-vertically propagating seismic SH waves. The superstructure modelled herein consists of a top mass supported by four columns on a rigid flat circular footing placed upon the surface of the arbitrarily shaped alluvial valley. Since it may be expected that the variation of the surface displacement amplitudes of the alluvial valley changes rapidly according to the increase in frequency of the incident SH waves, it is necessary to consider not only the translational vibration but also the torsional one of of the three-dimensional soil-structure interaction system even though the superstructure may be idealized to have no eccentric mass and rigidity disributions. The boundary conditions on the surface ground are treated as a mixed boundary value problem, which is reduced to a set of Fredholm integral equations. It is shown for the three-dimensional soil-structure interaction system that the torsional response of the structure has predominant effect on the relative response of the structure, and that the more closely the structure is located to the edge of the alluvial valley, the more pronounced the effect of incident angle of SH waves on the displacement amplitude of the structure becomes.