This work presents a method for determining the effective Young’s modulus (Eeffective) and Poisson ratio of small specimens of a ternary shape memory alloy (SMA), Cu-Al-Be. The alloys were synthesized uniformly and homogeneously using various concentrations of high purity metals and formed into slabs of different geometrical shapes. The phases and fractional quantities of each sub-alloy composing the SMA were determined using SEM/EDS data and the lever rule, and confirmed by matching computed and measured X-ray diffraction peak patterns. The Eeffective was determined using the rule of mixtures, employing elastic moduli obtained from Ab initio (Density functional theory) calculations. To address the challenge of determining Eeffective experimentally for small specimens, high frequency ultrasonic waves and vibration spectroscopy were used. The Eeffective was then used in a 3D finite element model to compute the vibrational spectrum’s resonance peaks, which were found to match those of the experimental vibrational response. The Eeffective was also compared to the pressure wave (P-waves) modulus recovered using non-contact ultrasound waves propagating through the sample’s thickness. Discrepancies mainly occurring for alloys with the β phase were resolved by determining its anisotropic spatial Young’s modulus. Overall, the presented method provides a comprehensive characterization of the mechanical properties of small alloy specimens.