The dissociation of CO2 in a geometrically symmetric dielectric barrier discharge has been analysed by means of numerical modelling. A time- and space-dependent fluid model has been used, taking into account the spatial variation of the plasma between the plane-parallel dielectrics covering the electrodes. The main features of the model, including an extensive reaction kinetics for the vibrational states of CO2, are given. The modelling studies have been performed for different applied voltages, discharge frequencies, pressures, gas temperatures, and relative permittivities of the dielectrics. The model calculations show that the discharges in the positive and negative half-cycles are different for the considered standard condition, leading to a spatially asymmetric distribution of the stable neutrals like CO molecules and O atoms. The generation of CO mainly takes place during the discharge pulses, and it is dominated by electron impact dissociation. The specific energy input obtained for the broad range of parameters considered and determined for residence times reported in the literature agrees well with the corresponding experimental values. In accordance with these experiments, the calculated degree of CO2 conversion has been found to increase almost linearly with the specific energy input. Remaining discrepancies between the measured and calculated energy efficiencies are discussed.