This paper describes a new surface electrical stimulation approach to the production of task-oriented functional hand and finger movements in people with upper extremity paralysis as the result of brain or spinal cord injury. The approach involves the need to first identify ("map") the distribution of the optimal electrical stimulation sites. Multi-channel electrical surface stimulation is then applied to obtain the desired motions. We describe here the grasping of a paper cup by the hand and three-digit pinching induced by this approach in a healthy subject as well as the results of a training trial in two adults with C6-level spinal cord injury.