The non-invasive cortical bone quality assessments using ultrasound axial transmission technique have attracted strong attention. The estimation of phase velocity and attenuation of absorbing plate should help the assessment. To get the high-resolution estimation, we employ an adaptive beamforming technique that uses an eigenvalue decomposition. The technique can estimate not only the phase velocities but also intensities of the multiple propagation modes separately. We situate two arrays in the whole array and compare the estimated intensities at the adjacent arrays. To remove unreliable estimates, we also situate sub-arrays with multiple sizes in the two arrays and evaluate the correspondences between the results with different sub-array sizes. The proposed method was evaluated by using numerical simulation. We used one transmitter and 28 receivers and a 5-mm-thick plate with longitudinal and shear wave velocities of 4430 m/s and 2120 m/s, respectively. The attenuations of the longitudinal and shear waves were 320 dB/MHz/m and 400 dB/MHz/m, respectively. The estimation error of the phase velocity and attenuation was 3.6 m/s and 2.4 dB/m, respectively. The proposed method accurately estimated the phase velocity and attenuation. We believe the method is suitable for bone quality assessments.