Methods of treating pain are disclosed, wherein a non-pulsed, low-frequency electrical current is applied to the nerve carrying the pain signals in order to suppress transmission of those signals. In desired embodiments, the current is applied in a direction transverse to the nerve axis. Such currents have been found not to induce motor-neuron recruitment, meaning these methods can treat pain without causing muscle spasm or other muscular responses. A cuff for applying such a current transverse to the nerve axis is also disclosed.