A non-invasive electrical stimulation device shapes an elongated electric field of effect that can be oriented parallel to a long nerve, such as a vagus nerve in a patient's neck, producing a desired physiological response in the patient. The stimulator comprises a source of electrical power, at least one electrode and a continuous electrically conducting medium in which the electrode(s) are in contact. The stimulation device is configured to produce a peak pulse voltage that is sufficient to produce a physiologically effective electric field in the vicinity of a target nerve, but not to substantially stimulate other nerves and muscles that lie between the vicinity of the target nerve and patient's skin. Current is passed through the electrodes in bursts of preferably five sinusoidal pulses, wherein each pulse within a burst has a duration of preferably 200 microseconds, and bursts repeat at preferably at 15-50 bursts per second.