Tensile strain development in high-density polyethylene (HDPE) geomembrane (GMB) liner systems in landfills was numerically investigated. A new constitutive model for municipal solid waste (MSW) that incorporates both mechanical creep and biodegradation was employed in the analyses. The MSW constitutive model is a Cam-Clay type of plasticity model and was implemented in the finite difference computer program FLAC™. The influence of the friction angle of the liner system interfaces, the biodegradation of MSW, and the MSW filling rate on tensile strains were investigated. Several design alternatives to reduce the maximum tensile strain under both short- and long-term waste settlement were evaluated. Results of the analyses indicate that landfill geometry, interface friction angles, and short- and long-term waste settlement are key factors in the development of tensile strains. The results show that long-term waste settlement can induce additional tensile strains after waste placement is complete. Using a HDPE GMB with a friction angle on its upper interface that is lower than the friction angle on the underlying interface, increasing the number of benches, and reducing the slope inclination are shown to mitigate the maximum tensile strain caused by waste placement and waste settlement.