In this work, simulation of beam propagation through atmospheric turbulence is made by means of the split-step method, including spatially separated two-dimensional phase screens, which represent the existing turbulence. These phase screens may be generated mainly by two techniques, namely fractal interpolation or in the spatial frequency domain. We report some important considerations to take into account in order to generate phase screens with enough accuracy to properly reproduce the structure function of the turbulence. It is shown that slight deviations from the theoretical structure function in the set of screens used along the propagation may increase in an appreciable way the statistical error inherent to any particular realization. Some comparisons are made with analytical results based on the second order Rytov approximation. One of the conclusions that may be clearly drawn from these comparisons is that beam wander effects are not included in these theories.© (2005) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.