Real modulus of elasticity of the soil usually increases with the depth of the soil due to the increase in overburden pressure. Therefore, incorporation of the effect of the soil inhomogeneity in the formulation to obtain the response of the machine foundations is an important and a necessary step. In this paper, equations that govern the dynamic behavior of the machine foundations and consider the inhomogeneity of the elastic foundation, particularly for Gibson type soil are derived by using variational principles. The coupled equations of the motion of the physical system are solved by applying iterative procedure, and the computer code developed for the numerical model can be run even on the small computers. (C) 1999 Elsevier Science Ltd. All rights reserved.