In this paper, anisotropic wave propagation theory was utilized to measure the slight anisotropy of a cold‐rolled aluminum plate. To reveal the slight anisotropy (texture) in such a medium, the deviation of the energy and phase velocity was taken into account. A numerical algorithm was developed to calculate the phase velocity from the measured energy velocity, and hence, to determine the elastic constant matrix of the cold‐rolled aluminum plate. It is found, from the measurements, that the rolled aluminum plate preserves slight transverse isotropy with the axis of symmetry along the rolling direction. The Young's modulus along the rolling direction is slightly smaller than those along the other two directions.