Dynamic behavior of two types of martensitic transformations during tensile deformation of Cu-Al-Ni shape memory alloy single crystal has been investigated using an acoustic emission waveform analysis. Two kinds of martensitic transformations consist of β1 ⇔ β1′ (structural change of DO3 to 18R) and β1 ⇒ γ1′ (structural change of DO3 to 2H), each of which is called super-elastic and thermo-elastic martensitic transformations, respectively. These two types of martensitic transformations could be obtained during tensile deformation because of different heat treatment. The rise time at the source (the source rise time) in finite elastic solid by the modified Takashima’s method was analyzed using the acoustic emission waveform detected during the martensitic transformation. The mean source rise time to the γ1′ phase was smaller than that to the β1′ phase before yielding and became the same after yielding. The former result means that the nucleation of the γ1′ phase is faster than that of the β1′ phase because of different crystallographic structure. The latter result is that the growth rate of the γ1′ phase is the same as that of the β1′ phase.