A complete set of second and third order elastic constants of the cubic austenite phase in CuAlNi shape memory alloy was determined by ultrasonic pulse-echo method. Because of the very high elastic anisotropy of the austenite phase (A=12.02), a negative Poisson ratio ν is obtained for loading the crystal in certain directions, e.g. ν 1 2 =ν 2 1 =-0.62 in the coordinate system [110], [110], [001]. Measurements of the third order elastic constants were carried out in nine selected specimen geometries (acoustic modes). The wave velocity was highly sensitive to the applied stress only in two shear modes. The onset of the stress-induced martensitic transformation (MT) was detected by acoustic emission (AE), ultrasonic wave velocity and attenuation measurements in given order. The acoustic emission was thus the most sensitive acoustic method for detection of early stages of the transformation.