Vagus nerve stimulation (VNS) is emerging as potential treatment for several chronic diseases, however, limited control of fiber activation to promote desired effects over side effects restricts clinical translation. Here we describe a new VNS method that relies on intermittent, interferential sinusoidal current stimulation (i2CS) through implanted, multi-contact epineural cuffs. In swine, i2CS elicits specific nerve potentials and end organ responses, distinct from equivalent non-interferential sinusoidal stimulation. Comparing experimental results with anatomical trajectories of nerve fascicles from end organs to the stimulation electrode indicates that i2CS activates organ-specific fascicles rather than the entire nerve. Experimental results and anatomically realistic, physiologically validated biophysical models of the vagus nerve demonstrate that i2CS reduces fiber activation at the focus of interference. Current steering and repetition frequency determine spatiotemporal pattern of vagal fiber activation, allowing tunable and precise control of neural and organ responses. In experiments in a cohort of anesthetized swine, i2CS has improved selectivity for a desired effect, mediated by smaller bronchopulmonary fibers, over a side effect, mediated by larger laryngeal fibers, compared to non-interferential sinusoidal or square pulse VNS.