In this article, we describe the use of a continuous-wave laser scanning method to generate non-dispersive surface acoustic wavepackets, which propagate along the sample surface without any waveform change. To achieve this goal, a coated linear elastic film on a non-linear substrate allows for careful balancing of dispersion and non-linearity effects. The scanning speed of the laser source and the thickness of the coated film were parametrically investigated to determine the optimal scanning speed for the generation of ultrasound for a given thickness of the coated film. In the first step, four different combinations of scanning speeds and the thickness of the coated film are presented to illustrate the generation of the narrowband ultrasound. The purpose of the scanning laser source is to effectively generate large amplitude ultrasound that takes the material into the nonlinear range. Further optimization through a careful matching combination of the scanning speed and the thickness of the coated film, whereby the dispersion effect was compensated entirely by the non-linearity effect, was used to generate non-dispersive ultrasonic wavepackets, which subsequently propagate with little distortion. The main findings of the simulations indicate that non-dispersive surface acoustic wavepackets for coated systems can be generated via the scanning laser source approach for specific values of scanning speed and thickness of the coated film.