High temperature superconducting (HTS) magnetic levitation (maglev) is a promising technology for future high-speed transit systems. Superconducting magnetic bearings are made of a permanent magnet guideway and HTS bulks (bulk-type) or stacks of 2G HTS tapes (stack-type). If the dynamic behavior of bulk-type HTS maglev systems has been well reported, there is little literature about the dynamics of stack-type HTS maglev system. To fill the gap, we built here an electromagnetic-mechanical model of a stack-type bearing. We used a segregated <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> -formulation finite element model to account for the nonlinear resistivity. The multi-layer structure of the HTS tape is either homogenized or modeled in detail. We studied the bearing dynamic response when subjected to different time-varying external magnetic fields mimicking the guideway irregularity and the vehicle speed. The results show that the induced current in the copper layer negatively impacts the stability. By extension, since it cannot account for the copper layer, the homogenized model is not suitable for such analysis. This work contributes to finding viable measures for improving the stability of stack-type HTS maglev systems.