Patterns of vertical movement in pelagic predators can be highly complex, reflecting behaviours such as foraging, thermoregulatory excursions and spawning. Here we used fast Fourier analysis to identify periodicity in the vertical movements of 6 basking sharks Cetorhinus maximus from archival tagging data that totalled 595 d. We analysed quantitatively fine-scale vertical movements of basking sharks over seasonal scales (May to February) and detected predominant periodicities related to the vertical movements of the sharks’ zooplankton prey. Normal and reverse diel vertical migration (DVM) represented the main periodic dive behaviour, occurring for 11 to 72% of individual track times. A tidal pattern of vertical movement, previously unreported for sharks, was also identified. A possible mechanism for this behaviour appears related to the shark exploiting tidally-induced aggregations of zooplankton prey at depth. The youngest shark tagged showed a markedly different pattern of vertical behaviour. Long-term data sets of swimming depth are becoming increasingly available for pelagic predators from pressure-sensitive data loggers. This study demonstrates the utility of signal processing techniques in objectively identifying both expected and unexpected periodicity in these continuous, high-resolution tracks.