Peripheral nerve stimulation (PNS) is an effective means to elicit sensation for rehabilitation of people with loss of a limb or limb function. While most current PNS paradigms deliver current through single electrode contacts to elicit each tactile percept, multi-contact extraneural electrodes offer the opportunity to deliver PNS with groups of contacts individually or simultaneously. Multi-contact PNS strategies could be advantageous in developing biomimetic PNS paradigms to recreate the natural neural activity during touch, because they may be able to selectively recruit multiple distinct neural populations. We used computational models and optimization approaches to develop a novel biomimetic PNS paradigm that uses interleaved multi-contact (IMC) PNS to approximate the critical neural coding properties underlying touch. The IMC paradigm combines field shaping, in which two contacts are active simultaneously, with pulse-by-pulse contact and parameter variations throughout the touch stimulus. We show in simulation that IMC PNS results in better neural code mimicry than single contact PNS created with the same optimization techniques, and that field steering via two-contact IMC PNS results in better neural code mimicry than one-contact IMC PNS. We also show that IMC PNS results in better neural code mimicry than existing PNS paradigms, including prior biomimetic PNS. Future clinical studies will determine if the IMC paradigm can improve the naturalness and usefulness of sensory feedback for those with neurological disorders.