Octopus arms, as well as other muscular hydrostats, are characterized by a very large number of degrees of freedom and a rich motion repertoire. Over the years, several attempts have been made to elucidate the interplay between the biomechanics of these organs and their control systems. Recent developments in electrophysiological recordings from both the arms and brains of behaving octopuses mark significant progress in this direction. The next stage is relating these recordings to the octopus arm movements, which requires an accurate and reliable method of movement description and analysis. Here we describe a semi-automatic computerized system for 3D reconstruction of an octopus arm during motion. It consists of two digital video cameras and a PC computer running custom-made software. The system overcomes the difficulty of extracting the motion of smooth, non-rigid objects in poor viewing conditions. Some of the trouble is due to the problem of light refraction in recording underwater motion. Here we use both experiments and simulations to analyze the refraction problem and show that accurate reconstruction is possible. We have used this system successfully to reconstruct different types of octopus arm movements, such as reaching and bend initiation movements. Our system is non-invasive and does not require attaching any artificial markers to the octopus arm. It may therefore be of more general use in reconstructing other non-rigid, elongated objects in motion.