Most studies of surface ground motion caused by earthquake have been based on the assumption that this motion is caused by the upward propagation of shear waves through a soil deposit from an underlying rock formation. However, much of the recorded strong ground motion from earthquakes has been caused by horizontally propagating Love and Rayleigh waves. In this study an irregular structure has been represented by a finite element model, which has been forced at one end to oscillate with the stresses corresponding to the displacements of fundamental Love and Rayleigh modes of periods from 2 sec down to 0.375 sec. The irregular structure represented by the finite element model is an alluvial valley with a layer of alluvium, 100 m thick, over Pierre Shale, 900 m thick. The side of this valley dips at an angle of 45°. As would be expected from the study of the upward propagation of shear waves, there are large amplifications of surface Love-wave and horizontal Rayleigh-wave motions within the alluvial valley at a period of 2 sec. However, these large amplifications do not occur at periods shorter than 2 sec because of three factors. First, at periods shorter than 2 sec, practically all of the energy of the fundamental Love and Rayleigh modes at the side of the alluvial valley is transferred within the alluvial valley to higher Love and Rayleigh modes; these modes do not have large surface displacements. Second, for this particular model of an alluvial valley, the horizontal surface amplitude of the fundamental Rayleigh mode at periods of approximately 2 sec is large compared with the vertical surface amplitude, whereas at periods of approximately 1 sec the vertical surface amplitude is large compared with the horizontal surface amplitude. Finally, at periods shorter than approximately 2 sec, damping of surface amplitudes of Love and Rayleigh modes within the alluvial valley is more effective. The method of considering the upward propagation of shear waves explicitly allows for only the last of these three factors.