Based on the theory of linear elastodynamics

and combined with the coordinate transformation

the dynamic governing equations for a half-plane inhomogeneous subgrade are developed. The dynamic response of a two-dimensional inhomogeneous subgrade subjected to moving loads is analyzed based on a semi-analytical method. Using Fourier series expansion

and assuming the series form of response function

the analytical expressions of various physical quantities are developed for the inhomogeneous subgrade subjected to moving loads

in which the shear modulus can arbitrarily change with depth. Assuming the shear modulus has an exponential distribution with the thickness

a parametric study is presented to illustrate the influence of the foundation soil inhomogeneity and load moving velocity as well as shear modulus at subgrade surface on the dynamical response of foundation soils. The calculated results are compared with the responses of a homogeneous subgrade

showing that the vertical displacement of soil decreases with the increase of the shear modulus at the surface of subgrade and the inhomogeneous gradient index

and increases with the increase of the load moving velocity. Under a moving load

the dynamic responses of inhomogeneous subgrade are significantly different from that of homogeneous subgrade.