A scattering problem by trapezoidal dikes with circular-arc foundation was studied. Effects of properties of SH waves and dike on maximum displacement (|uy|max|uy|max) were studied. Natural fixed-base frequency of foundation causes |uy|max|uy|max at the top surface of soft dike. Rigid body motion at quasi-resonance frequency causes |uy|max|uy|max at the hard dike top surface. This study provides a better understanding of the soil-structure interaction.