Knowledge of the force required to overcome deformation at the proportionality limit, yield point, as well as knowledge of the effect of selected factors on the characteristics during bending stress, have scientific and practical significance. They are the basis for designing tools for bending and accurately determining the stresses to which products and their parts may be subjected during use. This study analyzed the effect of selected factors on the selected characteristics, including the forces at the proportionality limit (FE) and yield point (FP). The chosen factors of this study were the wood species (Fagus sylvatica L. and Populus tremula L.), non-wood component (carbon and fiberglass), non-wood component position in the composition matrix (up and down), material thickness (6 mm, 10 mm, and 18 mm), and adhesive used (polyvinyl acetate and polyurethane), as well as their combined interaction. The results contributed to the advancement of knowledge necessary for the study and development of new materials with specific properties for their intended use. The results could improve the innovative potential of wood processing companies and increase their performance and competitiveness in the market.