There exist three fundamental physical quantities in the dynamic soil-foundation interaction problem. These are the real and imaginary parts of impedance, and the seismic exciting force. An integral equation formulation based on the dynamic Green's functions for an elastic medium is developed for use as a tool in analyzing the fundamental physical quantities. A limited number of the evaluation for them are available at present, most of which are restricted to the case of flat foundations because in case of the embedded foundation the enormous computational time is needed for calculation of the dynamic Green's functions. It is the objective of this work to remove the limitation by applying interrelations of the physical quantities to the boundary integral equation method. The displacement field is represented by the displacement component of the Green's functions and the source distribution at the interface of soil and foundations. Both of the imaginary part of the impedance and the static impedance are directly obtained by the source distribution. The real part of the impedance is indirectly calculated from them by the Hilbert transform. The seismic exciting force is represented as the product of the source distribution and the free-field motion through use of the reciprocal theorem. Therefore, the evaluation of the physical quantities reduces to the problem of determining the intensity of source distribution. The proposed method resolves a prevailing shortcoming in the analysis of the embedded foundation ; the necessity of calculation for the stress components of the dynamic Green's functions.