Seismic design of waste landfills has been a subject of intense research over the past two decades, primarily due to the severe environmental impact of a potential failure. The majority of the related studies have been focused on the stability assessment of landfills utilizing permanent deformation methods. However, previous investigations have not fully addressed the impact of the composite liner system on the seismic performance of the geostructure, mainly expressed as potential sliding development, which is greatly affected by the geometry and the resulting initial static stress state of the landfill. Therefore, the aforementioned issues are investigated via a detailed parametric study, where the dynamic behaviour of the composite liner system is examined both analytically and numerically. The conducted coupled analyses indicated that the most significant parameters of the complex dynamic response of waste landfills can be reduced in two ratios that comprise functions of the main characteristics of the geostructure and of the excitation. Moreover, two distinct failure patterns have been identified with respect to the characteristics of the distribution of the permanent displacements along the interface and the axial deformation along the geosynthetic. The occurrence conditions of these failure patterns can be determined in terms of the two abovementioned ratios as verified by the analytical results of the critical acceleration of a simple SDOF system.