Abstract: Multi-storey buildings and laminated rubber isolators are modelled as periodic systems in this paper. The receptance approach to periodic structure theory is applied to study the wave propagation and vibrational transmission into a base-isolated multi-storey building due to horizontal harmonic ground motion. The analysis is focused on the effects of the storey number of of the rubber, the mass of the intermediate steel plates and the structural parameters of the laminated rubber bearing. Numerical results are presented for the range of parameter values which encompass different situations encountered in real life.