Hand function can be restored in upper-limb amputees by equipping them with anthropomorphic prostheses controlled with signals from residual muscles. The dexterity of these bionic hands is severely limited in large part by the absence of tactile feedback about interactions with objects. We propose that, to the extent that artificial touch mimics its natural counterpart, these sensory signals will be more easily integrated into the motor plan for object manipulation. We describe an approach to convey tactile feedback through electrical stimulation of the residual somatosensory nerves that mimics the aggregate activity of tactile fibers that would be produced in the nerve of a native hand during object interactions. Specifically, we build a parsimonious model that maps the stimulus—described as time-varying indentation depth, indentation rate, and acceleration—into continuous estimates of the time-varying population firing rate and of the size of the recruited afferent population. The simple model can reconstruct aggregate afferent responses to a wide range of stimuli, including those experienced during activities of daily living. We discuss how the proposed model can be implemented with a peripheral nerve interface and anticipate it will lead to improved dexterity for prosthetic hands.