The propagation of optical plane waves through a one-dimensional Gaussian phase screen and a two-dimensional Gaussian extended medium are simulated numerically, and wave statistics are calculated from the data obtained by the numerical simulation. For instantaneous realization of a random medium, a simplified version of the random-motion model [77] is used, and for wave-propagation calculation the wave-kinetic numerical method and/or the angular-spectral representation of the Huygens-Fresnel diffraction formula are used. For the wave-kinetic numerical method, several different levels of approximations are introduced, and the region of validity of those approximations is studied by single-realization calculations. Simulation results from the wave-kinetic numerical method are compared, either with those from the existing analytical expressions for the phase-screen problem, or with those from the Huygens-Fresnel diffraction formula for the extended-medium problem. Excellent agreement has been observed. Extension to two-dimensional media with the power-law spectrum or three-dimensional problems is straight-forward. We may also deal with space-time correlations using, for example, Taylor's frozen-in hypothesis.