Acoustic-resonance spectroscopy was used to determine the complete elastic constants of a uniaxial-fiber-reinforced metal-matrix composite:​ boron-aluminum. This material exhibits orthotropic macroscopic symmetry and, therefore, nine independent elastic stiffnesses C_ij. The off diagonal elastic constants (C₁₂,C₁₃,C₂₃), which contain large errors when measured by conventional methods, were especially focused on. Good agreement emerged among present results, a previous pulse-echo study, and theoretical predictions using a plane-scattered-wave ensemble-average model. Attempts to measure the internal-friction "tensor" failed.