In order to understand and develop the knowledge about nonlinear behaviour of materials one need to combine some physical procedures, like theoretical modelling, simulations and experimental verification to get a better understanding of the materials. This Thesis work consists of two separate parts. The aim of the first part is to develop a numeric model to simulate acoustic wave propagation through a nonlinear mesoscopic material. The aim of the second part is to experimentally reconstruct stress-strain dependence for dynamic response of a thin nonlinear layer in order to verify analytical formulas.