Efficiency, functionality and performance of the grain grinding process are significantly influenced by phenomena that are difficult to describe and occur in the working area of the grinder. In a machine-based, multi-disc grinding of grain biomaterials, the design of the quasi-cutting unit, volumes, sections of transport/grinding holes, their motion and the design features of the discs (the grinding unit) must facilitate the functions of grinding in the inter-hole space (with minimum energy-consumption of the process and maximum efficiency) and minimising undesirable phenomena related to mixing and transport. The pre-requisite for optimisation of the quasi-cutting unit design is a mathematical model. Among many aspects of the problem, this study describes a sample procedure resulting in a filling model for a biomass grain quasi-cutting unit including an initial verification of the same under conditions of the evaluation of maize and triticale grain grinding efficiency, using an innovative multi-hole 5-disc and 7-disc grinder.