The paper presents mathematical models describing the moments of resistance to cutting on the cutting drum shafts in the biomass cutting process. The mathematical procedures described in the paper have been verified on a test stand developed and constructed by the authors, which reflects real conditions of the process of cutting plant material into pieces of specified lengths. Experimental verification proved that the developed mathematical models are adequate for drums of both cylindrical and conical constructions. The value of the average error did not exceed 13%. Following the mathematical elaboration and verification studies, the authors carried out calculations for machines currently available on the market that are equipped with drum cutting units. The calculations were carried out for the most commonly cut material, i.e. for maize, straw and green plant materials. The obtained results confirm the complexity of the problem arising from a wide range of numerical values of cutting resistance, which is contained in the range of 400–1,800 nm. The compiled database can be practically applied in the selection of machines for specific field works, and the mathematical models developed and verified in the study can be applied at the stage of designing new designs of cutting drums used in forage harvesters.