Abstract. Comparisons of amplitudes of wave variations of atmospheric characteristics obtained using direct numerical simulation models with polarization relations given by conventional theories of linear acoustic-gravity waves (AGWs) could be helpful for testing these numerical models. In this study, we performed high-resolution numerical simulations of nonlinear AGW propagation at altitudes 0–500 km from a plane wave forcing at the Earth's surface and compared them with analytical polarization relations of linear AGW theory. After some transition time t_e (increasing with altitude) subsequent to triggering the wave source, the initial wave pulse disappears and the main spectral components of the wave source dominate. The numbers of numerically simulated and analytical pairs of AGW parameters, which are equal with confidence of 95 %, are largest at altitudes 30–60 km at t > t_e. At low and high altitudes and at t < t_e, numbers of equal pairs are smaller, because of the influence of the lower boundary conditions, strong dissipation and AGW transience making substantial inclinations from conditions, assumed in conventional theories of linear nondissipative stationary AGWs in the free atmosphere. Reasonable agreements between simulated and analytical wave parameters satisfying the scope of the limitations of the AGW theory prove the adequacy of the used wave numerical model. Significant differences between numerical and analytical AGW parameters reveal circumstances when analytical theories give substantial errors and numerical simulations of wave fields are required. In addition, direct numerical AGW simulations may be useful tools for testing simplified parameterizations of wave effects in the atmosphere.