Abstract: A sliding composite lumped parameter model is established based on the results obtained with complex-shaped formulations of embedded foundation oscillating on an elastic half-space. Horizontally dynamic responses of a arbitrarily shaped and complicatedly embedded foundation are calculated by making use of this model and formulas (supported by results of comprehensive experimental and numerical analysis), which are developed by the theory of elastic half-space for computing the dynamic stiffness and damping coefficients of foundations harmonically sliding oscillating on a homogeneous half-space. Agreement is found between the proposed model and the theory of elastic half-space for sliding oscillations with an error of 22.9%. The advantage of the composite lumped parameter model is to compute the dynamic responses of arbitrarily shaped and complicatedly embedded lumped foundations sliding oscillating on a homogeneous half-space readily considering all oscillation frequencies, realistic range of Poisson’s ratios(ν≤0.48), all foundation base shapes(excluding annular) and complicated embedment.