Composite liners are commonly used in modern landfills. The translational slide failure modes, in which the back slope of the failure surface slides along the inside of waste dump and the bottom slope slides along the liner interface, may become one of the composite failure modes. In this study, we considered the effects of leachate based on the methods for stability calculation of such failure modes. We assumed that the failure surface through the inside of the waste dump was an active failure surface. Then, we used the limit equilibrium analysis method and discussed different positional relationships between leachate levels and specific interfaces, in order to obtain the calculation methods for different situations. The results of analysis and calculation show that, when the leachate water levels rose, the failures of waste dumps changed from translational slides along the liner interface to composite failures through the inside of waste dumps and the bottom liner. In practical engineering examples, the failure and instability occurred precisely because the leachate water level was too high.