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In the classical approaches, used in Central Europe in practice, cutting forces and cutting power in sawing processes of timber are commonly computed by means of the specific cutting resistance kc. It needs to be highlighted that accessible sources in handbooks and the scientific literature do not provide any data about wood provenance, nor about cutting conditions, in which cutting resistance has been empirically determined. In the analyses of sawing processes, the use of a model with elements of fracture mechanics involved is an alternative way. In this work, predictions of the newly developed model (FRAC_MOD) for the circular sawing machine are presented. Thanks to this modern approach, it was possible to reveal the usefulness of the FRAC_MOD, using experimental results data on fracture toughness and shear yield stresses of both Polish pine (Pinus sylvestris L.) and Czech beech wood (Fagus sylvatica L.). The achieved results were compared to the forecasted values obtained with classical models (CLAS_PL and CLAS_CZ), which are commonly applied in Central European sawmills. The carried out analyses allowed us to discover undesired effects in the form of underestimation of cutting power when applying the CLAS_PL and CLAS_CZ models. For that reason, the FRAC_MOD cutting model could be suggested for the prediction of energetic effects in cases of dynamical analyses and even unsteady cases.