During massive rainfall conditions, the clogging of a poorly designed drainage layer of the veneer cover system has an adverse impact on its stability and durability. This influences the overall performance of the municipal solid waste (MSW) landfill. The water clogged in the drainage layer of the landfill cover system is termed as an internal seeper. The level of internal seeper in the drainage layer is defined as the immersion ratio (Ir), which is the most influencing parameter affecting the cover system stability. The present study discusses the uplifted-floating (uf) failure mode of the veneer cover system, which might occur due to the hydraulic pressure put forth by the internal seeper. The expression of the factor of safety against uplifted-floating failure mode (FSuf) is derived using the force equilibrium approach. The stability of the veneer cover system against uplifted-floating (uf) failure can be ensured by providing adequate cover soil-layer thickness (h) above the drainage layer. The current study presents the optimum cover soil-layer thickness (h) corresponds to the factor of safety (FSuf) ≥ 1.50 against uplifted-floating (uf) failure. The results are portrayed in the form of design charts, that are developed to estimate the cover soil-layer thickness (h) for different stability numbers (c/ γsatH ) and immersion ratios (Ir). The established design charts show the effects of the ratio of slope length of cover soil to a height of landfill (L/H) and the internal friction angle of cover soil (ϕ ) on the allowable cover soil-layer thickness (h). © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.