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Using a previous mechanical characterization of two types of material, several lab-test work have been done. The data shows the particle size distribution of these tests, all the inputs and the model simulation presented in the related paper to this data base. The new mathematical approach use the operative conditions and the feed particle size distribution to obtain a product, which is compared with the lab-test results, An improved approach is presented to model the product particle size distribution resulting from grinding in high-pressure roll crusher with the aim to be used in standard high-pressure grinding rolls (HPGR). This approach uses different breakage distribution function parameter values for a single particle compression condition and a bed compression condition. Two materials were used for the experiments; altered Ta-bearing granite and a calc-silicate tungsten ore. A set of experiments was performed with constant operative conditions, while varying a selected condition to study the influence of the equipment set-up on the model. The material was comminuted using a previously determined specific pressing force, varying the feed particle size, roll speed and the static gap. A fourth group of experiments were performed varying the specific pressing force. Experimental results show the high performance of the comminution in a high-pressure environment. The static gap was the key in order to control the product particle size. A mathematical approach to predict the product particle size distribution is presented and it showed a good fit when compared to experimental data. This is the case when a narrow particle size fraction feed is used, but the fit became remarkably good with a multi-size feed distribution. However, when varying the specific pressing force in the case of the calc-silicate material, the results were not completely accurate. The hypothesis of simultaneous single particle compression and bed compression for different size ranges and with different parameters of the distribution function was probed and reinforced by various simulations that exchanged bed compression parameters over the single particle compression distribution function, and vice versa.