Tissue level mechanics is a key factor to be investigated to improve the knowledge of how the overall trabecular structure reacts to loading and overloading. The aim of this study was to develop a new device for measuring the mechanical competence of single trabeculae in the post-yield region for both tensile and bending tests, characterized by high accuracy and precision, and to assess the effect of testing mode, donor age and material composition. A novel approach for measuring the displacement and deformation was developed (accuracy error of 0.3% and a precision of 2.7%). A total of 30 samples from two bovine femora of different ages (from <3-year-old and 14-year-old cows) were tested in tension or bending, while average material properties have been acquired by means of Raman spectroscopy. A group of trabeculae was tested in bending after treatment for collagen degradation. As a result, a complete set of post-yield properties has been reported. The results highlight significant differences between tensile and bending groups, with higher values for the bending test mode for yield strain, ultimate strain and post-yield work and lower for the elastic modulus. Significant higher values were found for the old donor (differences in the range of 30–60%) for elastic modulus, yield stress and ultimate stress as well as for material properties measured by Raman spectroscopy. We quantified that changes in materials properties induced by collagen degradation corresponded to a substantial decrease (up to 120% for post-yield work) of mechanical competence, both in the elastic and inelastic region.