The surface acoustic waves, i.e., surface phonons may have huge potential for future spintronic devices, if coupled to other waves (e.g., spin waves) or quasiparticles. In order to understand the coupling of acoustic phonons with the spin degree of freedom, especially in magnetic thin film-based heterostructures, one needs to investigate the properties of phonons in those heterostructures. This also allows us to determine the elastic properties of individual magnetic layers and the effective elastic parameters of the whole stacks. Here, we study frequency versus wavevector dispersion of thermally excited SAWs in CoFeB/MgO heterostructures with varying CoFeB thickness by employing Brillouin light spectroscopy. The experimental results are corroborated by finite element method-based simulations. From the best agreement of simulation results with the experiments, we find out the elastic tensor parameters for CoFeB layer. Additionally, we estimate the effective elastic parameters (elastic tensors, Young’s modulus, Poisson’s ratio) of the whole stacks for varying CoFeB thickness. Interestingly, the simulation results, either considering elastic parameters of individual layers or considering effective elastic parameters of whole stacks, show good agreement with the experimental results. These extracted elastic parameters will be very useful to understand the interaction of phonons with other quasiparticles.