We discuss the suitability of laser-based resonant ultrasound spectroscopy (RUS) for the characterization of soft shearing modes in single crystals of shape memory alloys that are close to the transition temperatures. We show, using a numerical simulation, that the RUS method enables the accurate determination of the $c^{\prime }$ shear elastic coefficient, even for very strong anisotropy, and without being sensitive to misorientations of the used single crystal. Subsequently, we apply the RUS method to single crystals of three typical examples of shape memory alloys (Cu-Al-Ni, Ni-Mn-Ga, and NiTi), and discuss the advantages of using the laser-based contactless RUS arrangement for temperature-resolved measurements of elastic constants.