A frequent goal of hand movement is to touch a moving target or to make contact with a stationary object that is in motion relative to the moving head and body. This process requires a prediction of the target's motion, since the initial direction of the hand movement anticipates target motion. This experiment was designed to define the visual motion parameters that are incorporated in this prediction of target motion. On seeing a go signal (a change in target color), human subjects slid the right index finger along a touch-sensitive computer monitor to intercept a target moving along an unseen circular or oval path. The analysis focused on the initial direction of the interception movement, which was found to be influenced by the time required to intercept the target and the target's distance from the finger's starting location. Initial direction also depended on the curvature of the target's trajectory in a manner that suggested that this parameter was underestimated during the process of extrapolation. The pattern of smooth pursuit eye movements suggests that the extrapolation of visual target motion was based on local motion cues around the time of the onset of hand movement, rather than on a cognitive synthesis of the target's pattern of motion.