Structural finite element analysis (FEA) was performed on a straight 40-tape Twisted Stacked-Tape Cable (TSTC) surrounded with a solid copper core to investigate the stress state of the tape-stack under cyclic transverse compressive Lorentz loads up to the tenth cycle. Two worst-case stack orientations, 45 degree and 90 degree, were investigated. In addition, the stack was modeled as simply placed into the core or soldered to the core. Since annealing of the copper core can occur during machining; the stress state of the stack was studied as a function of yield strength of the copper. The results showed that if the copper was strong enough, the stress state of the stack remained unaltered and low up to 300 kN/m cyclic transverse compressive loading. However, when the copper was fully annealed, the plastic deformation accumulated from cyclic loading more significantly affected the stress distribution in the stack. If the tape-stack was simply placed into the core, the tapes can move and slide after each loading cycle. The averaged stress went down for the first few cycles, and then plateaued. However, when the stack was soldered to the core, the stack had less room to move, and therefore the stress state remained at higher values and was less affected by cyclic loading. Additionally, when producing the stack, the tapes at the edge may not align perfectly, and this would introduce additional stress concentration. The misalignment of the stack was studied, and the results showed that this effect caused higher stress in the stack. The numerical modeling presented provides a technique to simulate cyclic loading of TSTC cable. Besides, the information on the stress state of the tape-stack can be used to investigate the behavior of more recently developed cable designs and optimize future configurations.