Atmospheric‐pressure dielectric barrier discharges (DBDs) in argon with admixtures of small amounts of hexamethyldisiloxane (HMDSO) have been analysed by means of numerical modelling. A time‐dependent, spatially one‐dimensional fluid‐Poisson model has been used, which takes into account the spatial variation of the discharge plasma between the plane‐parallel dielectrics covering the electrodes. Main features of the model, including the reaction kinetics for HMDSO, are given. Good agreement with related experimental studies of the ignition voltage for HMDSO amounts of up to 200 ppm and the temporal course of the discharge current for conditions typical of deposition experiments is obtained by the model calculations when assuming that 30% of the reactions of HMDSO with excited argon atoms, with a rate coefficient of 5.0 × 10−10 cm3/s, lead to the production of electrons due to Penning ionization. The modelling results for constant frequency f = 86.2 kHz and applied voltage Ua = 4 kV show that the electrical energy dissipated in the DBD decreases with an increasing amount of HMDSO and enable the determination of the energy absorbed per HMDSO molecule on the basis of their energy balance. The analysis of the plasma–chemical processes also makes clear that collision processes of HMDSO with excited argon atoms and molecules leading to neutral reaction products are essential for the formation of thin polymer films.