The surface acoustic wave velocity has been measured on a-plane (c-propagation) and c-plane oriented bulk aluminum nitride (AlN) single crystals using the S11-parameter method in the frequency range 160-360 MHz. The SAW velocity is 5760 m/s for both orientations. From comparison of this value with the simulations using various elastic constants of AlN available in literature, we estimated the elastic constant C44 to be 122 +/- 1 GPa.