Nondestructive evaluation of elastic properties plays a critical role in condition monitoring of thin structures such as sheets, plates or tubes. Recent research has shown that elastic properties of such structures can be determined with remarkable accuracy by utilizing the dispersive nature of guided acoustic waves propagating in them. However, existing techniques largely require complicated and expensive equipment or involve accurate measurement of an additional quantity, rendering them impractical for industrial use. In this work, we present a new approach that requires only a pair of piezoelectric transducers used to measure the group velocities ratio of fundamental guided wave modes. A numerical model based on the spectral collocation method is used to fit the measured data by solving a bound-constrained nonlinear least squares optimization problem. We verify our approach on both simulated and experimental data and achieve accuracies similar to those reported by other authors. The high accuracy and simple measurement setup of our approach makes it eminently suitable for use in industrial environments.