Context. Rapid blue- and redshifted excursions (RBEs and RREs) may play an important role in mass-loading and heating the solar corona, but their nature and origin are still debatable.

Aims. We aim to model these features to learn more about their properties, formation, and origin.

Methods. We created a realistic three-dimensional (3D) magnetohydrodynamic model of a solar plage region. Synthetic Hα spectra were generated and the spectral signatures of these features identified. The magnetic field lines associated with these events were traced, and the underlying dynamic was studied.

Results. The model reproduces many properties of RBEs and RREs well, such as spatial distribution, lateral movement, length, and lifetimes. Synthetic Hα line profiles, similarly to observed ones, show a strong blue- or redshift as well as asymmetries. These line profiles are caused by the vertical component of velocities higher than 30 − 40 km s⁻¹, which mostly appear in the height range 2 − 4 Mm. By tracing magnetic field lines, we show that the vertical velocity that causes the appearance of RBEs or RREs is always associated with the component of velocity perpendicular to the magnetic field lines.

Conclusions. The study confirms the hypothesis that RBEs and RREs are signs of Alfvénic waves with, in some cases, a significant contribution from slow magneto-acoustic modes.