Abstract: A new sliding composite lumped parameter model (CLPM) is established based on the theory of surface foundation oscillation on an elastic half-space. With the new model (CLPM), horizontally dynamic responses of a complicatedly-shaped surface foundation is calculated and the computing results are in good agreement with the results obtained by the formulas (supported by results of comprehensive experimental and numerical analysis), which have been developed by the theory of elastic half-space for computing the dynamic stiffness and damping coefficient of foundations harmonically swaying oscillating on a homogeneous half-space, the amplitude difference is only 9.2% and 0.8% in lateral direction (x) and longitudinal direction (y), respectively. The new model can be used to easily determine the dynamic responses of arbitrarily shaped lumped foundations (except annular shape) with all range of oscillation frequencies and all range of Poisson’s ratios on homogeneous half-spaces under the horizontal perturbation load.