This chapter is devoted to the formulation of the dynamics of linear discrete systems excited by the acceleration of the supports; this type of excitation is relevant in earthquake engineering, or during the qualification of space systems on a shaking table. In the first part of this chapter, the equations governing the motion of a structure subjected to a single-axis excitation are derived from Hamilton’s principle. The equations are then transformed in modal coordinates, with the introduction of the modal participation factor and the effective modal mass; the modal expansion of the dynamic mass (relating the support reaction to the support acceleration) is derived and the issue of modal truncation is discussed (missing mass). The second part of this chapter is devoted to the more delicate case of multi-axis excitation which brings the issue of differential displacements. The cascade analysis of primary-secondary structures concludes this chapter. A set of problems is proposed.