The ultrasonic properties like ultrasonic attenuation, sound velocity in the group VIB transition metal diborides like CrB₂ and MoB₂ have been studied along unique axis at room temperature. The second- and third order elastic constants (SOEC & TOEC) have been calculated for these diborides using Lennard–Jones potential. The velocities $V_L$ and $V_{S2}$ increase with the angle from the unique axis and $V_{S1}$ has maximum at $45^\circ$ with unique axis of the crystal. The inconsistent behaviour of angle dependent velocities is associated to the action of second order elastic constants. Debye average sound velocities of these compounds are increasing with the angle and have maximum at $55^\circ$ with unique axis at room temperature. Hence when a sound wave travels at $55^\circ$ with unique axis of these materials, then the average sound velocity is found to be maximum. The mechanical properties of CrB₂ are better than MoB₂, because CrB₂ has low ultrasonic attenuation comparison than MoB₂. The comparison of calculated ultrasonic parameters with available theoretical/experimental physical parameters gives information about classification of these compounds.