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In this paper, ultrasonic properties like ultrasonic attenuation, sound velocities, acoustic coupling constants and thermal relaxation time have been studied in hexagonal structured metals Gadolinium (Gd), Terbium (Tb), Dysprosium (Dy), Holmium (Ho), Erbium (Er) and Thulium (Tm) along unique axis at room temperature. For the evaluations of ultrasonic properties, second-and third-order elastic constants have been computed also. The peculiar behavior of these metals is found at 55° due their least thermal relaxation time and highest Debye average velocity. Dy is more ductile, stable, perfect metal in comparison to other chosen metals due to its lowest value of attenuation. So we predict that Dy is most suitable lanthanide metals for material science and engineering.

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