In this study, a unified analytical model is presented for out-of-plane vibration of sandwich plates with arbitrary boundary conditions. It is assumed that the displacement of the core plate varies linearly along the thickness. Based on the Kirchhoff hypothesis, the displacement solutions of base and constrained plates of sandwich plate are expressed as a two-dimensional Fourier series supplemented with several one-dimensional Fourier series. On this basis, the vibration distribution characteristics of sandwich plates induced by metro trains are obtained by applying the measured vibration acceleration on the boundaries of sandwich plates. Besides, the dynamic response of sandwich plates whose material parameters vary with coordinate positions can be solved well by the proposed method. According to the vibration distribution characteristics of sandwich plates, the material parameter distributions are purposively designed, which reduces the train-induced vibration on the sandwich plate significantly. Furthermore, some cases for various material parameter distributions of sandwich plates are given to study the vibration mitigation performance of these sandwich plates. Finally, the relationships between the vibration mitigation performance of the improved sandwich plates and their coordinate-dependent material parameters are fully investigated.