Near‐fault fling steps might cause severe damage to near‐fault structures such as bridges or base‐isolated buildings. Therefore, the accurate simulation of ground displacements including fling steps based on fault models is an important issue not only for seismological but also for engineering purposes. The discrete wavenumber (DWN) method (e.g., Bouchon, 2003) has been established as a method to calculate complete elastic wavefield, including permanent displacement for a homogeneous or a layered half‐space. However, the accuracy of the permanent displacements calculated by the DWN method is influenced by the selection of parameters, such as the imaginary part of the complex frequency and the subfault size in the case of extended sources. The objective of this study is to clarify the requirement for these parameters for the accurate simulation of fling‐step displacements to further enhance the use of the DWN method. Honda and Yomogida (2003) also addressed the issue of calculating fling‐step displacements using the DWN method; however, their study was focused on cases in which a large amount of seismic moment is released at depth. This study was focused on fling‐step displacements due to rather shallow slip, in which the fault distance was as small as several meters in an extreme case, motivated by recent damaging earthquakes such as the 2016 Kumamoto, Japan, earthquakes. The ground displacements including fling steps were calculated by the DWN method and compared with the analytical solutions for the static displacements (Okada, 1985, 1992), both for point sources and extended sources in a homogeneous half‐space. According to the results, following recommendations were made. For the imaginary part of the complex frequency, , with can be recommended, with the understanding that the waveforms are effective only within the range of . For extended sources, the subfault size should be as small as 0.5 times the fault distance to accurately simulate fling steps.