Seismic excitations with long-period frequencies often coincide with the fundamental natural frequencies of tall buildings, causing resonance and significant structural responses. These resonant motions impact modular vertical transportation (VT) systems, such as traction-driven elevators comprising highly flexible long slender continua (LSC) and discrete masses. Here an analytical and numerical model to predict the dynamic responses of VT systems under long-period earthquake excitations is developed. The model captures the time-varying natural frequencies due to changing rope lengths and the complex resonance interactions when seismic frequencies align with system modes. Numerical simulations demonstrate significant coupling between rigid body motions and LSC resonance, highlighting critical resonance conditions. These findings provide insights for designing resonance mitigation strategies, enhancing the seismic resilience and operational safety of VT systems in high-rise buildings.