Traction drive elevator installations employ ropes of variable length as a mean of car and counterweight suspension. The inertial and elastic characteristics of elevator suspension systems depend on the rope construction and vary slowly during the elevator travel. The system suffers from vibrations caused by various sources of excitation. This paper presents the analysis of the dynamic response of the suspension system employing traditional steel wire ropes as well as ropes constructed of aramid fibers. The equations describing the lateral response of the system subjected to a boundary periodic excitation are solved numerically. The results show that the entire rope is subjected to repetitive low frequency transient resonances. Consequently, the structural integrity of the suspension ropes is compromised. The issue of active vibration control and the feasibility of the integration of shape memory alloy elements within the suspension rope design are discussed.