The modelling of high pressure grinding rolls is described by the population balance model, a mass balance which includes several functions that are related to the mineral characteristics, material kinetics and operative conditions of the device. The breakage distribution function is one of these functions and refers to the way in which the daughter particles are generated by the process of comminution. The piston-die press is presented as a methodology to determine the breakage distribution function of two different materials, from the mechanical response point of view: altered granite and a cal-silicate material. The aim is to determine the relation between the operative conditions and the mineral characteristics in order to explain and predict the breakage function parameters. The materials were characterised using XRD and single compression strength tests. The altered granite is a brittle material, which generates more fines under single compression conditions compared to bed compression conditions, mainly due to the mineral composition and the response of the material to the breakage action. The cal-silicate material shows a normal trend in its breakage behaviour. As is expected, the mineralogical characterisation is a useful tool to predict the values of the parameters of the breakage distribution function.