In this paper, a transfer matrix and a three-dimensional dynamic response of a layered half-space to an arbitrary buried source are derived with the aid of a technique which combines the Laplace and two-dimensional Fourier transforms in a rectangular coordinate system. This method is clear in concept, and the corresponding formulas given in the paper are simple and convenient for marine seismic prospecting and other fields’ applications. An example is presented and the calculated results are in good agreement with those of the finite element method (FEM). In this paper, a transfer half and a three-dimensional dynamic response of a layered half-space to an arbitrary buried source are with the aid of a technique which combines the Laplace and two-dimensional Fourier transforms in a rectangular coordinate system. method is clear in concept, and the corresponding formulas given in the paper are simple and convenient for marine seismic prospecting and other fields’ applications. An example is presented and the calculated results are in good agreement with those of the finite element method (FEM) .