Singular rock columns or blocks resting on tilted irregular rough joints can be found in rock masses in various geological environments. Their stability can be estimated based on traditional limit equilibrium approaches. However, the geometry of these rock blocks may not be regular, which makes uneasy stability computation tasks. Previous studies have addressed toppling mechanisms of rock blocks having various geometries and accounting for eroded or non-sharp-edged corners. Moreover, an analytical approach to consider the influence of regular roughness on the base of the block on its toppling response has been recently proposed. In this study, the authors advance towards a better understanding on how irregular roughness may affect the stability against toppling of cylindrical physical models with an irregular rough base in the lab, which are analyzed based on proposed analytical expressions. The study shows consistent empirical and analytical results regarding the toppling response of the samples tested, which indicates that toppling of blocks with irregular rough bases can be studied based on analytical formulations. Moreover, this roughness can slightly influence the instability mechanism of toppling, as shown in an illustrative example.