In advanced functional materials, where the prestress can initialize phase transitions or other structural changes, the effect of the increasing load on an acoustic wave velocity is substantial and can provide important information on the undergoing physical phenomena. In this paper, a novel method for contactless measurements of acousto-elastic parameters is presented. The contactless arrangement, based on the concept of laser-ultrasound, enables an accurate detection of small changes of the velocities of surface acoustic waves in various directions. Because of this contactless arrangement, the changes of the sample shape during the loading do not affect the results, which can be assumed as the main source of inaccuracy for classical contact methods. The experimental device and its control system is described in detail, and its application possibilities and limits are shown on examples of shape memory alloys.