The propagation of a deformation along a flexural beam or plate depends on material properties, geometrical conditions like the beam cross-section, effects of stiffening or softening due to external stress, and last but not least the mode of the wave including its polarization. The time-of-flight (TOF) of acoustic waves is influenced by any of the above listed parameters. This effect is utilized in ultrasonic NDE and structural health monitoring applications. It was shown in earlier publications that the solutions of wave equations for a linear chain model consisting of identical mass points, subject to a direction and distance dependent potential, show the dispersion properties and dependencies on externally applied stress of the lowest longitudinal and transversal plate modes. In the model presented here anharmonic potentials are introduced. The potentials are represented by torsional springs at each mass point and linear springs between them. Dynamic equations are derived, based on interactions with next and second next neighbors. The results obtained with the developed model are compared with experimental observations concerning the reaction of the TOF for the lowest Lamb modes in an aluminum plate under variable in plane stress. The developed models are capable to demonstrate general aspects of the mode and frequency dependence of the acousto-elastic coefficients for the lowest symmetric and antisymmetric Lamb waves. The introduced anharmonicities allow furthermore for a close approximation of the experimental findings. [ABSTRACT FROM AUTHOR]