This study is concerned with the free vibration analysis of thick plates on elastic foundation using modified Vlasov model. The effects of the subsoil depth, aspect ratios, the ratio of subsoil depth to span of the plate and the value of the vertical deformation parameter within the subsoil on the frequency parameters of plates on elastic foundations are investigated. An eight-neded, 24 degrees of freedom quadrilateral finite element (PBQ8) based on Mindlin plate theory is used for the analysis. The first six natural frequency parameters are presented to show the effects of the parameters considered in the study. It is concluded that the subsoil depth is more effective on the frequency parameters of plates resting on elastic foundation than the other parameters considered in this study.