The vibration analysis of a plate on an elastic foundation is an important problem in engi- neering. It is the interaction of a plate with the three-dimensional half space and the plate is usually loaded from both the upper and lower surfaces. The contact pressure from the soil can not be predefined. According to Lamb's solution for a single oscillating force acting on a point on the surface of an elastic half space, and the relevant approximation formulae, a relation between the local pressure and the de- flection of the plate has been proposed. Based on this analysis, the reaction of the soil can be represented as the deformation of the plate. Therefore, the plate can be separated from the soil and only needs to be divided by a number of elements in the analysis. The following procedure is the same as the standard fi- nite element method. This is a semi-analytical and semi-numerical method. It has been applied to the dy- namic analysis of circular or rectangular plates on the elastic half space, at low or high frequency vibra- tion, and on rigid, soft or flexible foundations. The results show that this method is versatile and highly accurate.