In order to design effective shredding machines dedicated to shredding wood-based waste, information about the mechanical properties of materials subjected to shredding is necessary. A number of mechanical properties of particleboard, oriented strand boards, and medium-density fibreboards in the aspect of shredding process have been experimentally determined in the article. The influence of material type, blade geometries, and cutting depth on cutting force and elasticity coefficient were analysed. Blade geometries reflect different phases of rotation of the cylindrical wood chipper’s knife. It has been shown that a knife with the most favourable geometry is characterized by the lowest values of the stiffness coefficient for each of the materials. This is the geometry of the cylindrical wood chipper’s knife exactly halfway into the cutting process. By contrast, the least favourable geometry is characterized by a knife corresponding to the beginning of the cutting process. Among the tested materials, the medium density board requires the most energy to change its structure, and the laminated particleboard requires the least. The presented results can be a set of input data necessary to model the work required to implement the cutting process, but also enable validation of existing cutting models.