The problem of control of rigid body response of structural systems such as nuclear islands, which are mounted on a gird of bearings with three dimensional damping and stiffness properties, is analyzed. A parametric study is carried out to show the effects of the dimensionless parameters of the foundation on the transmissibilities of the structure due to harmonic ground motion. The characteristics of an optimal base isolation are discussed and results are presented in a form which may be of use in preliminary designs.