The paper presents the influence of the martensitic phase transition on hypersonic thermally excited surface acoustic waves propagating in Cu–14%Al–4%Ni (wt%) shape memory alloy. Non-destructive and non-contact testing using Brillouin light scattering spectroscopy permitted determination of the elastic constants of austenite versus temperature. Experimental results obtained for martensite were interpreted using the proposed model of the cubic to orthorhombic martensitic phase transition based on the Landau model of a first-order phase transition. Additionally we adopted the approximation of the domain structure of martensite by a polycrystalline sample using the Voigt–Reuss–Hill procedure of averaging the elastic constants.