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 stiffnessesCij. 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. ©1995 American Institute of Physics.