The closed-form analytical solution for the effect of foundation flexibility on system response amplitude and system frequency of dynamic soil-structure interaction is presented. The wave function expansion method through a two-dimensional (2D) out-of-plane model, in which a single-degree-of-freedom (SDOF) system is supported by a semi-circular rigid-flexible composite foundation embedded into a homogeneous half-space subjected to plane SH waves, is used. The accuracy of the analytical solution is verified by comparing the results of the rigid foundation-SDOF model with the results of the flexible foundation-SDOF model. The numerical results are also performed and analyzed. It is shown that foundation flexibility has a strong effect on the system amplitude and system frequency. The analysis shows the dynamic response of the foundation and the relative response of the superstructure are very different to that of the rigid foundation results, especially for the case of small shear-velocity of the flexible layer and the small size of the rigid core. The displacement of the rigid core is always larger than that of the rigid foundation. Moreover, the rigid foundation assumption cannot provide the correct deformation of the structure near the base in the actual soil-structure interaction. The peak of the relative response of the superstructure is also always smaller than that of the rigid foundation, which means the rigid foundation may overestimate the effects of scattering of incident waves and the effective input motion of the foundation. The flexibility of the foundation also significantly affects the system frequency. When considering the flexibility in the analysis, the system frequency defined by the peak of the relative response of the superstructure will shift toward lower frequencies compared with that of the rigid foundation, and the amount of shift is highly dependent on the foundation flexibility. The larger the foundation flexibility, the larger the shift value is. The largest shift value can reach 38.9% of the rigid foundation system frequency.