Invariant representations of stimulus features are thought to play an important role in producing stable percepts of objects. In the present study, we assess the invariance of neural representations of tactile motion direction with respect to other stimulus properties. To this end, we record the responses evoked in individual neurons in somatosensory cortex of primates, including areas 3b, 1, and 2, by three types of motion stimuli, namely scanned bars and dot patterns, and random dot displays, presented to the fingertips of macaque monkeys. We identify a population of neurons in area 1 that is highly sensitive to the direction of stimulus motion and whose motion signals are invariant across stimulus types and conditions. The motion signals conveyed by individual neurons in area 1 can account for the ability of human observers to discriminate the direction of motion of these stimuli, as measured in paired psychophysical experiments. We conclude that area 1 contains a robust representation of motion and discuss similarities in the neural mechanisms of visual and tactile motion processing.