In this paper we present a one- dimensional fluid model to study the properties of very small dielectric barrier discharges ( DBD), which can be used as microchip plasma sources for analytical spectrometry. The influence of the pressure on this kind of discharge was investigated to obtain more insight in the variations of discharge current and the differences in particle densities that arise when operating at different pressures. The studied discharge gas is helium and is described with passive He background atoms, He+ and He-2 (+) ions, He metastable atoms, higher excited states of He, He-2 * excimers and electrons. We show that the plasma activity, expressed in discharge current, is remarkably higher for pressures ranging from 50 to 140 mbar. For most pressures the calculated maximum current density is about 0.1 A cm(-2), whereas in the range from 50 to 140 mbar the maximum current density is about 0.3 A cm(-2). We also report how the plasma densities alter at different operating pressures, with spatially averaged densities at maximum current ranging from about 10(16) m(-3) to 10(18) m(-3), depending on the plasma species, and identify the main underlying processes, which are responsible for these evolutions.