The elasticity of both the austenite and martensite states of a NiMnGa Heusler alloy was investigated by using a continuous wave method. A magnetic field was used to detwin the martensite. The symmetrized elastic constants of both austenite and martensite were determined by exiting different modes of wave propagation. In austenite, the shear elastic constant (C<sub>11</sub>-C<sub>12</sub>)/2 equals 7Gpz, which means the alloy is very soft as is typically the case in near second order shape memory alloys. Similarily, in martensite, (C<sub>11</sub>-C<sub>12</sub>)/2 equals 9GPa. Moreover, in the martensitic state the two rhombohedral elastic constants, C<sub>44</sub> and C<sub>66</sub>, equaling 51GPa and 49GPz, respectively are almost the same.