This study contains three components: measurement, modeling, and inverse modeling to get the fiber elastic constants. The studied composite consisted of 70 vol % continuous uniaxial graphite fibers in a magnesium matrix. By ultrasonic‐velocity methods, we measured the composite’s complete orthotropic‐symmetry (nine‐independent‐component) elastic‐constant tensor: Cij in Voigt contracted notation. Approximately, the composite shows transverse‐isotropic symmetry. For a model, we used a wave‐scattering method in the long‐wavelength limit. The model requires two inputs: the two isotropic matrix elastic constants and the five anisotropic fiber elastic constants. We measured the first and guessed the second based on graphite‐fiber elastic constants reported by others. This guess gave good measurement‐model agreement only for C11, C22, and C33. Especially, the shear moduli Cii (i=4,5,6) agreed poorly (a 20% difference). Using inverse modeling—calculating fiber properties from measured matrix properties and measured composite properties—we estimated the anisotropic fiber elastic constants. For the fiber we predict a Young‐modulus anisotropy of 12 and a principal Poisson ratio range of 0.03–0.37.