We continually move our body and our eyes when exploring the world, causing our sensory surfaces, the skin and the retina, to move relative to external objects. In order to estimate object motion consistently, an ideal observer would transform estimates of motion acquired from the sensory surface into fixed, world-centered estimates, by taking the motion of the sensor into account. This ability is referred to as spatial constancy. Human vision does not follow this rule strictly and is therefore subject to perceptual illusions during eye movements, where immobile objects can appear to move. Here, we investigated whether one of these, the Filehne illusion, had a counterpart in touch. To this end, observers estimated the movement of a surface from tactile slip, with a moving or with a stationary finger. We found the perceived movement of the surface to be biased if the surface was sensed while moving. This effect exemplifies a failure of spatial constancy that is similar to the Filehne illusion in vision. We quantified this illusion by using a Bayesian model with a prior for stationarity, applied previously in vision. The analogy between vision and touch points to a modality-independent solution to the spatial constancy problem.