Copper production is an essential component of the Chilean economy. During the extraction process of copper, large quantities of waste materials (tailings) are produced, which are typically stored in large tailing ponds. Thickened Tailings Disposal (TTD) is an alternative to conventional tailings ponds. In TTD, a considerable amount of water is extracted from the tailings before their deposition. Once a thickened tailings layer is deposited, it loses water and it shrinks, forming a relatively regular structure of tailings blocks with vertical cracks in between, which are then filled up with "fresh" tailings once the new upper layer is deposited. The dynamic response of a representative column of this complex structure made out of tailings blocks with softer material in between was analyzed using a periodic half-space finite element model. The tailings' behavior was modeled using an elasto-plastic multi-yielding constitutive model, and Chilean earthquake records were used for the seismic analyses. Special attention was given to the liquefaction potential evaluation of TTD.