Neurophysiological and behavioral studies suggest that the peripersonal space is represented in a multisensory fashion by integrating stimuli of different modalities. We developed a neural network to simulate the visual-tactile representation of the peripersonal space around the right and left hands. The model is composed of two networks (one per hemisphere), each with three areas of neurons: two are unimodal (visual and tactile) and communicate by synaptic connections with a third downstream multimodal (visual-tactile) area. The hemispheres are interconnected by inhibitory synapses. We applied a combination of analytic and computer simulation techniques. The analytic approach requires some simplifying assumptions and approximations (linearization and a reduced number of neurons) and is used to investigate network stability as a function of parameter values, providing some emergent properties. These are then tested and extended by computer simulations of a more complex nonlinear network that does not rely on the previous simplifications. With basal parameter values, the extended network reproduces several in vivo phenomena: multisensory coding of peripersonal space, reinforcement of unisensory perception by multimodal stimulation, and coexistence of simultaneous right- and left-hand representations in bilateral stimulation. By reducing the strength of the synapses from the right tactile neurons, the network is able to mimic the responses characteristic of right-brain-damaged patients with left tactile extinction: perception of unilateral left tactile stimulation, cross-modal extinction and cross-modal facilitation in bilateral stimulation. Finally, a variety of sensitivity analyses on some key parameters was performed to shed light on the contribution of single-model components in network behaviour. The model may help us understand the neural circuitry underlying peripersonal space representation and identify its alterations explaining neurological deficits. In perspective, it could help in interpreting results of psychophysical and behavioral trials and clarifying the neural correlates of multisensory-based rehabilitation procedures.