High resolution large-eddy simulations (LES) were carried out to simulate the turbulent flow of the atmospheric boundary layer during an idealized strong-wind event in order to verify discrete gust models like the one-minus-cosine law which are used in the design process of aircraft and wind turbines. Furthermore existing gust models will be improved and new analytical approaches will be developed to approximate gusts more accurately. Mean gust shapes of the three wind speed components are calculated by means of virtual measurements of the turbulent wind speed at different heights above ground to analyze both the one- and two-dimensional characteristics of discrete gusts. One-dimensional results of the mean gust shapes show significant differences compared to the classical one-cosine gust model like a steeper increase and decrease as well as a rather constant middle part. Results obtained from previous mast measurements, however, show the same main gust characteristics as the present LES gusts. Two-dimensional mean gust shapes have not been calculated from field measurements yet. The results obtained from the LES data show elliptically shaped contours with different aspect ratios for different gust diameters and heights above ground. For both, one- and two-dimensional mean gust shapes, mathematical approximations are presented as alternative approach to the classical gust models in order to be able to reproduce the mean gust shapes for future applications. © 2016 The Authors.