Neuroscientific research on pleasant touch has focused on the C-tactile pathway for gentle stroking and has successfully explained how these sensory fibers transmit information about affective social touch to the brain and induce sensations of pleasantness. The C-tactile social/affective touch hypothesis even proposes that C-tactile fibers form a privileged pathway underlying social touch. However, deep pressure is a type of touch commonly considered pleasant and calming, occurring in hugs, cuddling, and massage. In this paper we introduce a paradigm for studying pleasant deep pressure and propose that it constitutes another important form of social touch. We describe development of the oscillating compression sleeve (OCS) as one approach to administering deep pressure and demonstrate that this touch is perceived as pleasant and calming. Further, we show that deep pressure can be imaged with functional magnetic resonance imaging (MRI) using the air-pressure-driven OCS and that deep pressure activates brain regions highly similar to those that respond to C-tactile stroking, as well as regions not activated by stroking. We propose that deep pressure constitutes another social touch pathway of evolutionary importance signaling the close proximity of conspecifics.