Apparatus for multi-channel transverse epidural spinal cord stimulation uses a multi-channel pulse generator driving a plurality of electrodes mounted near the distal end of a lead. These electrodes are mounted in one or more lines, generally perpendicular to the lead axis, and have a planar surface along one surface of the lead. The lead is implanted adjacent to spinal cord dura mater with the electrodes transverse and facing the spinal cord. Pulses generated by the pulse generator for each channel are not simultaneous but are selectively offset in time and may be of equal or varying amplitude and of equal or varying duration. When the pulses given by the stimulator channels are offset in time and have sufficient amplitude and duration, overlapping areas of stimulation of the spinal area can be obtained. In the overlapping areas of stimulation, the frequency of stimulation is double the frequency of the pulses given by the each stimulator channel separately. Changes in pulse duration and magnitude permit shifting the electrical stimulation field and the resulting paresthesia pattern after installation to accommodate improper lead placement or postoperative dislocation and to minimize unwanted motor responses.