We assess the kinematic and dynamic accuracies of a finite-difference frequency-domain method for qP wave modelling in transversally isotropic acoustic media with tilted symmetry axis. This method was developed as a tool for frequency-domain full-waveform inversion which requires accurate traveltime and amplitude modelling. The modelling method is based on the parsimonious mixed-grid method which requires 5 grid points per wavelength in homogeneous media to mitigate numerical dispersion. We compare seismograms computed with the acoustic frequency-domain method with that provided by the complete solution of the transversally isotropic elastic wave equation. As expected we observed strong traveltime and amplitude mismatches in the case of strongly anisotropic materials such as zinc crystals. For weak anisotropy, we obtain a reasonable agreement although slight delay of the acoustic wide-angle reflections was observed in the case of a two-layer medium. The footprint of these inaccuracies in full-waveform inversion will need to be assessed before considering application to real data.