Groundwater quality can be deteriorated by leachate that seeps through the landfills. Placing a low permeable barrier beneath the landfill is a cost-effective approach to protect the subsurface environment. Recently local soil and/or waste materials (fly ash and flushed silt) amended with clay have emerged as an effective barrier to restrict and delay the leachate migration to the subsurface environment. One of the most critical selection criteria for landfill liners is hydraulic conductivity (Ks≤10−7  cm/s), which often varies during the field construction of the liners owing to nonuniform compaction efforts. Failure to achieve the desired compaction leads to the random distribution of hydraulic conductivity within the liner. The movement of contaminants through a landfill liner becomes more complex due to the random variations in the hydraulic conductivity within the liner. To address this, a probabilistic analysis has been conducted to investigate the movement of contaminants in the landfill liner, considering the stochastic hydraulic conductivity scenario. Stochastic hydraulic conductivity realizations of four different composites (bentonite amended sand, flushed silt, fly ash, and locally available natural soil) were generated by varying the standard deviation (�) of lognormal distribution in hydraulic conductivity and horizontal (X) and vertical (Z) correlation lengths. The performance of the landfill liner is evaluated by conducting a series of numerical experiments in HYDRUS 2D/3D in terms of breakthrough time, peak concentration, and solute mass distribution in the liner. � is identified in an inverse correlation with the breakthrough time, and a value between 0.25 and 0.75 should be maintained to achieve a breakthrough time>30  years. The ratio of X/Z majorly governed the performance of the liner, and it is concluded that a higher ratio leads to better service life. At least a value of X/Z=5 must be maintained while ensuring that X should not be less than 2. A smaller value of Z would be favorable for both peak concentrations and the breakthrough time. Amongst all composites and all stochastic combinations, natural soil amended with 30% bentonite outperforms with a delayed breakthrough time and lower peak concentrations.