Matrix equations of rigid‐body motion for a general isolation system are presented and conditions for decoupling translational and rotational motions are discussed. The effective rotational and translational stiffnesses of a set of isolators arbitrarily oriented with respect to the center of mass of an isolated rigid body are developed by matrix techniques. Influence coefficients for determining loadings on the isolator's elastic axes owing to arbitrary g loads at the system center of mass are also presented in matrix form. The application of the matrix techniques presented to the design of vibration isolation systems is illustrated through an example.