A packed bed dielectric barrier discharge (DBD) is widely used for plasma catalysis applications, but the exact plasma characteristics in between the packing beads are far from understood. Therefore, we study here these plasma characteristics by means of fluid modelling and experimental observations using ICCD imaging, for packing materials with different dielectric constants. Our study reveals that a packed bed DBD reactor in dry air at atmospheric pressure may show three types of discharges, i.e. positive restrikes, filamentary microdischarges, which can also be localized between two packing beads, and surface discharges (so-called surface ionization waves). Restrikes between the dielectric surfaces result in the formation of filamentary microdischarges, while surface charging creates electric field components parallel to the dielectric surfaces, leading to the formation of surface discharges. A transition in discharge mode occurs from surface discharges to local filamentary discharges between the packing beads when the dielectric constant of the packing rises from 5 to 1000. This may have implications for the efficiency of plasma catalytic gas treatment, because the catalyst activation may be limited by constraining the discharge to the contact points of the beads. The production of reactive species occurs most in the positive restrikes, the surface discharges and the local microdischarges in between the beads, and is less significant in the longer filamentary microdischarges. The faster streamer propagation and discharge development with higher dielectric constant of the packing beads leads to a faster production of reactive species. This study is of great interest for plasma catalysis, where packing beads with different dielectric constants are often used as supports for the catalytic materials. It allows us to better understand how different packing materials can influence the performance of packed bed plasma reactors for environmental applications.