We present results from the numerical study of ULF waves generated by the ionospheric feedback instability in density cavities. The goal of the study is to explain several spectral features of ULF waves detected on the ground in close vicinity of intense discrete auroral arcs. These features include (1) localization of the waves packages across the ambient magnetic field, (2) variation of the wave frequency in relatively small amplitude waves, and (3) presence of several discrete harmonics in the spectrum of the relatively large amplitude waves. Time‐dependent, two‐dimensional simulations based on the two‐fluid MHD model performed in the dipole, axisymmetrical geometry of the ambient magnetic field with realistic parameters of the plasma density in the ionosphere and the magnetosphere demonstrate that the ionospheric feedback instability inside the density cavity indeed provides a good, quantitative explanation of these features of ULF waves observed at high latitudes during substorm onsets.