The rocking motion of real bodies under external excitation can be often modeled by means of the theory of rigid body dynamics, neglecting the elastic deformations. Several studies paid attention to the dynamics of one block, under deterministic or stochastic excitation, whereas only few works focused on the case of two stacked blocks. In this paper the general problem of stacks with more than two rigid blocks is analyzed, typical of monumental ancient columns made of multiple stone blocks and also of stacks of drums filled with various material. Differing from previous papers, a vector based approach is adopted to write the equations of motion in a straightforward manner. Assuming non sliding rocking, the rotation angles are the Lagrangian parameters appearing in the equations of motion.Taking advantage of the Lagrange equations, the vector equation of motion is derived in a smartway.The impact has been accounted for by means of the conservation of angular momentum. Finally, the model is applied to the evaluation of seismic safety of the stack. © 2013 Taylor & Francis Group, London, UK.