Analytical solutions for space and time evolution of uplift pressures acting on the impervious lining of stilling basins are obtained. Uplift variations are forced by random fluctuating pressures generated by a hydraulic jump. The model, aimed at portraying real life behavior of stilling basins at the toe of high spillways, accounts for arbitrary forcing pressures and is referred to experimental evidence. A safe design criterion is given for stability of the lining with reference to the worst foreseeable conditions within the basin.