When combined in the lining and covering of waste-containment facilities, soil and geosynthetic components protect the environment by acting as a hydraulic barrier. Equipment loading may significantly increase the tensile stress induced in geosynthetic components, leading to a potential stability problem. Large equipment loadings may also result in a localized circular slip surface during construction operations. New analytical method based on discrete element modelling is proposed for estimating the distribution of tensile force developed in the individual geosynthetic components of the lining system and for evaluating the safety factor of slope failure due to equipment loading. The analytical results of an example are presented to demonstrate the applicability of the analytical method for the lining system of a waste landfill. The analyses of the example show that equipment loading provide a substantial increase in the tensile forces of the geosynthetic components of a lining system and that the possibility of shallow failure due to equipment loading increases as the slope becomes steeper. This method is a useful tool for analysing the lining system of waste landfills with complex lining components.