A computational multiple scattering simulation method was applied to analyze the characteristics of the ultrasonic shear wave that propagates in unidirectional carbon-fiber-reinforced epoxy composites with its polarization direction parallel to the fibers. The numerical simulations were carried out for regular as well as random fiber arrangements and for different fiber volume fractions. The results were combined with the one-dimensional theory describing the macroscopic propagation behavior, in order to identify the phase velocity and the attenuation coefficient of the composite. The phase velocity and the attenuation coefficient were found to depend significantly on the fiber volume fraction, but less so on the fiber arrangement in the frequency range examined here. Furthermore, the present analysis showed a good agreement with the experimental data.