Pre-stellar cores are defined to be the stage of star formation that preceeds the formation of a hydro-static protostar. We have observed a number of cores believed to be pre-stellar in nature in the submillimetre continuum with SCUBA on the JCMT. 37 cores were detected at 850 μm - 13 of them with high signal-to-noise. Radial density profiles of these 13 show flattened inner regions and sharp boundaries consistent with some models of the pre-collapse phase of protostar formation. Simple models are fitted to the core radial density profiles to assess their stability against collapse.