In this paper results of simulations of non-contact elastic wave generation in the composite panel based on acoustic to elastic wave transformation are presented. For this purpose simulations of acoustic wave generation and processing are based on the FEM method in COMSOL. Elastic wave generation and propagation are based on the spectral element method (SEM) in the time domain. The SEM model utilises time-varying acoustic pressure distributions calculated in the FEM. The SEM allows to simulate the interactions of elastic waves with the delamination. Damage localization is based on RMS elastic wave energy maps. In this research a panel made of carbon fibre-reinforced polymer composite is investigated. Research related to low-frequency air-coupled transducer (ACT) is presented. The utilisation of low-frequency waves allows for the reduction of the effects of the wave attenuation in composite material. The proposed combination of FEM and SEM gives an efficient tool for the simulation of non-contact wave generation for non-destructive testing analysis.