A non-invasive electrical stimulator 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 contact with the electrodes. The conducting medium is also in contact with an interface element that may conform to the contour of a target body surface of the patient when the interface element is applied to that surface. When the interface element is made of insulating (dielectric) material, and disclosed stimulation waveforms are used, the power source need not supply high voltage, in order to capacitively stimulate the target nerve. The stimulator produces a peak pulse that is sufficient to produce a physiologically effective electric field in the vicinity of a target nerve.