We propose extending the concept of spatial constancy to haptic perception. In vision, spatial constancy refers to the conversion of retinotopic signals into spatiotopic representations, allowing the observer to perceive space independently of his or her own eye movements, or at least partly so. The problem would seem at least as important in haptic perception, where sensory surfaces undergo even more complex movements in space. Here we develop a methodology for studying haptic spatial constancy, which involves a tactile display mounted on a mobile platform, and which allows us to decouple movements of the sensory surface—in this case the fingertip—from movements of objects on the fingertip. Using this apparatus, we find evidence for only weak haptic spatial constancy.