Nonlinear wave propagation has, for the last couple of decades, become an increasingly more important tool in medical ultrasound imaging. Creating ultrasound images from echoes in the second harmonic frequency band provides a major enhancement to the image quality, reducing body wall reverberation and also reducing perturbations from off-axis echoes.The aim of this study has been to make a fast implementation of nonlinear wave simulation in ultrasound, based on the Propose method, and investigate its agreement with the state-of-the art simulation tool, Abersim. Agreement between the methods has been investigated for a typical cardiac probe in the fundamental and second harmonic frequency band.The comparison showed good agreement for phase, amplitude, wave form and beam profile. Some overestimation of the center lobe in the beam profile was found, but this is expected for quasilinear methods.A fast implementation for simulation of nonlinear wave propagation in ultrasound has been made, based on the Propose method. The new implementation and is performing simulations in the second harmonic frequency band 74% -- 93% faster than the original implementation.