The slopes of open-pit mines are often at risk of failure. To identify this hazard, stability analyses are performed. An important element of these stability analyses is the reliable selection of input parameter values for the calculations. This selection is difficult because the slopes of the open pit are disturbed by mining activities. In such conditions, rheological processes, intensified by weathering, develop in open-pit slopes. This study is aimed at setting the strength parameters for the stability analysis of open-pit slopes with a developed slide process, using the random set method. The study was performed on the example of the open pit of the Bełchatów lignite mine, central Poland. A four-stage methodology, according to the random set method, was proposed. The methodology covered the following: site investigation, sensitivity analyses, shear strength reduction (SSR) analyses using numerical calculations, and probability analyses of the factor of safety (FoS) calculation results. The setting of the input parameters took into account the peak and residual strength parameters for each lithological unit in the physical model of the open-pit slope. Samples for laboratory tests were taken from the cores of nine test boreholes. The sensitivity analysis included all peak and residual strength parameters for each lithological unit in the body. As a result of the sensitivity analysis, specific strength parameters were adopted that would have a great impact upon the results of the calculations. Selected sets of parameter values were then used for the FoS calculations. The resultant FoS values revealed the probable slide planes. The positions of the slide planes were consistent with the interpreted slide surfaces based on the control boreholes and terrain observations. Knowledge of the slide planes positions and the values of the strength parameters enabled the designing of a securing approach for this landslide, and the taking of preventive measures to reduce this risk.