The acoustic wave propagator method has been developed and extended since 2000 for investigating the propagation of acoustic and flexural waves. The boundaries are usually introduced by defining the mechanical properties in the wave transmission path. This was found to be highly efficient but slightly inaccurate, especially when a boundary-smoothing technique is used to weaken the discontinuity and maintain the numerical stability. In this paper, an image source method is implemented during modelling, which simulate the boundary reflection by placing virtual sources emits similar signals at the same time. Compared with the results of several previous papers, this is found to provide a more accurate solution for studying wave propagation under different boundary conditions.