Computationally expensive finite element (FE) methods are generally used for indirect evaluation of tissue mechanical properties of trabecular specimens, which is vital for fracture risk prediction in the elderly. This work presents the application of reduced-basis (RB) methods for rapid evaluation of simulation results. Three cylindrical transiliac crest specimens (diameter: 7.5 mm, length: 10–12 mm) were obtained from healthy subjects (20 year-old, 22 year-old, and 24 year-old females) and scanned using microcomputed tomography imaging. Cubic samples of dimensions were extracted from the core of the cylindrical specimens for FE analysis. Subsequently, a FE solution library (test space) was constructed for each of the specimens by varying the material property parameters: tissue elastic modulus and Poisson’s ratio, to develop RB algorithms. The computational speed gain obtained by the RB methods and their accuracy relative to the FE analysis were evaluated. Speed gains greater than 4000 times, were obtained for all three specimens for a loss in accuracy of less than 1% in the maxima of von-Mises stress with respect to the FE-based value. The computational time decreased from more than 6 h to less than 18 s. RB algorithms can be successfully utilized for real-time reliable evaluation of trabecular bone elastic properties.