The paper presents a sound critical estimate of mathematical models presently used for the process of compaction of fine-grained materials. It shows the mathematical model of compaction developed by the authors, which was used to formulate the program of computer simulation of the process. The examples of computer simulation experiments of compaction of selected fine-grained materials regard the results of the experiments made by the authors on variability of external friction occuring in this process. Simulation examination presented in the paper crucially contributed towards the original method of selection of rational compaction technologies of fine-grained materials developed by the authors.