A vibration model to investigate the influence of building lateral vibration on the dynamic response of hoist ropes in an elevator system is presented in this paper. This model describes the coupled lateral-longitudinal dynamic response of the ropes in terms of non-linear partial differential equations that accommodate the non-stationary nature of the system. Subsequently, a discrete model with quadratic and cubic non-linear terms describing the modal interactions in the system is derived. It is shown that the building sway results in a distributed inertial load acting upon the hoist ropes which in turn may lead to resonance and modal interactions between the lateral modes and the fundamental longitudinal mode.