External cues bias human attention and the perception of subsequent targets. Little is known about how cue properties, such as depth, influence insect attention. One robust cue to depth is stereoscopic disparity, the difference in the position of an object in the views of the two eyes. Praying mantises are known to use disparity to judge the distance to prey and are therefore ideal insect models to investigate its role in attention. We investigated how three cue properties- position, duration and stereoscopic disparity affect mantis selective attention towards subsequent targets. We fitted mantises with 3D glasses and presented them with a cue in 2D or in 3D, followed by two 3D stimuli: a high contrast target and a distractor at different contrasts. Our results show that cue position and distractor contrast had the most influence on responses to targets, with no strong effect of disparity. Compared to the Uncued condition, cues in two of our disparity conditions reduced target responses if presented on the opposite side of the screen, when the distractor was absent. The cues affected subsequent selective attention even when they did not themselves attract head saccades, suggesting covert but not overt attention to the cues. Our results show that the position of prior cues can affect mantis selective attention and add further evidence for the complexity of attention-like processes in insects.