The stability inside the waste, internal stability, and co-stability between the elements of the insulation system and the landfill bed should be considered in the landfill design. The stresses and the resulting deformations in both mineral and geosynthetic materials of the insulation system must be controlled in the design, so that an unpredictable flow path is not created. Besides, long-term durability in the insulation system should be considered. An evaluation of the durability of the system requires knowledge of the interaction between the components and the waste as a settling object. The numerical modeling methods can be used to evaluate the local instability. In this study, a landfill constructed in the UK has been modeled in ABAQUS finite element platform and was verified with the results of obtained data from precision instruments at the landfill site. Then, by applying the earthquake excitations, the seismic behavior of the solid waste landfill under Far-Field and Near-Field earthquakes and their effect on the durability of the landfill wall system were investigated. The outputs include maximum displacement, maximum stress, the most critical state, and investigation of yield stress and rupture of the geomembrane layer. The results indicated that in the landfill wall, the maximum displacement occurs in the waste section. It occurs especially between the boundary of natural soil and waste. It was also observed that the geomembrane layer under the earthquake loadings had experienced some ruptures.