Lateralization of hand use in primates has been extensively studied in a variety of contexts, and starts to be investigated in other species and organs in order to understand the evolution of the laterality according to different tasks. In elephants, the orientation of the movements of the trunk has been observed mainly in feeding and social contexts, in free conditions. However, little is known about the influence of task complexity on trunk laterality. In this study, we compared the lateralization of the trunk in two conditions: standardized and free. We offered granules to six African elephants on each side of an opened trapdoor to create a constraining environment and reported the different behaviours employed and their orientation. In addition, we observed the same individuals in free conditions and noted the lateralization of the use of their trunk. We revealed a common right side preference in all our elephants, both in standardized and free conditions. This side bias was stronger in our constraining task, adding evidence for the task complexity theory. We finally described laterality in new behaviours in the literature on elephants, such as pinching, gathering or exploration with the trunk.