A model developed for a dielectric barrier discharge (DBD) in helium, used as a new spectroscopic source in analytical chemistry, is presented in this paper. The model is based on the fluid approach and describes the behavior of electrons, He+ and He+2 ions, He metastable atoms, He atoms in higher excited levels, and He2 dimers. The He ground-state atoms are regarded as background gas. The characteristic effect of charging/discharging of the dielectrics which cover both electrodes is also simulated. Typical results of the model include the distribution of potential inside the plasma (and the potential drop across the dielectrics), the electric current and gap voltage as a function of time for a given applied potential profile, the spatial and temporal number-density profiles of the different plasma species, and the relative contributions of the mechanisms of their production and loss.