A number of factors have been proposed to influence within and between species variation in handedness in non-human primates. In the initial study, we assessed the influence of grip morphology on hand use for simple reaching in a sample of 564 great apes including 49 orangutans Pongo pygmaeus, 66 gorillas Gorilla gorilla, 354 chimpanzees Pan troglodytes and 95 bonobos Pan paniscus. Overall, we found a significant right hand bias for reaching. We also found a significant effect of the grip morphology of hand use. Grasping with the thumb and index finger was more prevalent in the right compared to left hand in all four species. There was no significant sex effect on the patterns of handedness. In a subsample of apes, we also compared consistency in hand use for simple reaching with previously published data on a task that measures handedness for bimanual actions. We found that the ratio of subjects with consistent right compared to left hand use was more prevalent in bonobos, chimpanzees and gorillas but not orangutans. However, for all species, the proportion of subjects with inconsistent hand preferences between the tasks was relatively high suggesting some measures may be more sensitive in assessing handedness than others.