Interactions between the body and the environment occur within the peripersonal space (PPS), the space immediately surrounding the body. The PPS is encoded by multisensory (audio-tactile, visual-tactile) neurons that possess receptive fields (RFs) anchored on the body and restricted in depth. The extension in depth of PPS neurons' RFs has been documented to change dynamically as a function of the velocity of incoming stimuli, but the underlying neural mechanisms are still unknown. Here, by integrating a psychophysical approach with neural network modeling, we propose a mechanistic explanation behind this inherent dynamic property of PPS. We psychophysically mapped the size of participant's peri-face and peri-trunk space as a function of the velocity of task-irrelevant approaching auditory stimuli. Findings indicated that the peri-trunk space was larger than the peri-face space, and, importantly, as for the neurophysiological delineation of RFs, both of these representations enlarged as the velocity of incoming sound increased. We propose a neural network model to mechanistically interpret these findings: the network includes reciprocal connections between unisensory areas and higher order multisensory neurons, and it implements neural adaptation to persistent stimulation as a mechanism sensitive to stimulus velocity. The network was capable of replicating the behavioral observations of PPS size remapping and relates behavioral proxies of PPS size to neurophysiological measures of multisensory neurons' RF size. We propose that a biologically plausible neural adaptation mechanism embedded within the network encoding for PPS can be responsible for the dynamic alterations in PPS size as a function of the velocity of incoming stimuli. NEW & NOTEWORTHY Interactions between body and environment occur within the peripersonal space (PPS). PPS neurons are highly dynamic, adapting online as a function of body-object interactions. The mechanistic underpinning PPS dynamic properties are unexplained. We demonstrate with a psychophysical approach that PPS enlarges as incoming stimulus velocity increases, efficiently preventing contacts with faster approaching objects. We present a neurocomputational model of multisensory PPS implementing neural adaptation to persistent stimulation to propose a neurophysiological mechanism underlying this effect.