The application of two distinct physical concepts to the phenomena of rupture of dry agglomerates has been discussed. The classical theory proposed by Rumpf states that particle separation occurs when the adhesion forces are supplanted by the applied removal force, causing a simultaneous breakage of interparticle links along the rupture plane. Kendall and co-workers argue that this concept overestimates the energy necessary for breakage and propose that separation occurs from the nucleation of cracks in ’defects’ previously present in the agglomerate structure, with the energy consumption being proportional to the formation of the new surfaces. Two different kinds of dry agglomerates of the same material, filtration cakes and tumbling drum granules, had their rupture stresses experimentally estimated in laboratory conditions. These values were then used for discussing the theories of Rumpf and Kendall. The results indicate that neither theoretical approach could represent the two practical situations : Rumpf’s theory seems to be more adequate for the cake removal process whilst Kendall’s theory explains better the granule crushing mechanism. The conditions at the time of agglomerate formation could explain these observations, as they are reasonably well connected to the fundamental assumptions of the respective theoretical approaches.