The nondestructive testing of composite structural parts is often conducted via ultrasonic testing for the purpose of detecting damage by tracking wave velocity scattering phenomena. Additional information on the test part can be obtained by identifying its elastic constants. These constants can also be related to the part’s residual strength. This paper will present a technique to invert the ultrasonic guided wave dispersion properties to determine the elastic constants of a composite part. The inversion is obtained by matching the experimental phase velocity dispersion curves to Semi-Analytical Finite Element models. The approach is applied to a non-contact scanning system using air-coupled ultrasonic transducers for mapping impact damage in a stiffened composite aerospace panel. An efficient method for the extraction of the experimental phase velocity dispersion curves will be presented based on the analysis of the phase spectra of the received waves in a single-input dual-output system, enabling dispersion measurements from only two receiving points, as opposed to a series of receiving points required for 2D Fourier Transform techniques.