An alternative approach to measuring the complete anisotropic elastic constants cij(sij) of an orthorhombic‐symmetry material is proposed. This approach requires measurements along only principal directions: 〈100〉. In this approach, a pulse‐echo (megahertz‐frequency) method was used to measure c11, c22, c33, c44, c55, and c66. A resonance (kilohertz‐frequency) method was used to measure three elastic compliances: s11, s22, and s33. Combining the cii with the sii, the complete sets of cij and sij were obtained. This approach avoids the troublesome, error‐prone determination of off‐diagonal cij(sij) by the usual measurements along nonprincipal directions. The approach was applied to a boron‐aluminum composite where the off‐diagonal terms remain uncertain. In principle, the approach applies to any orthorhombic‐symmetry material.