The gaze cueing effect is the tendency for people to respond faster to targets appearing at locations gazed-at by others compared to locations gazed away from by others. However, although the gaze cueing effect has been studied extensively and has implications for a variety of theoretical and clinical contexts, much is still unknown about the cognitive mechanisms underlying its emergence. Formal evidence accumulation models provide the dominant account of the cognitive processes underlying speeded decisions, however, they have never been applied to understand the gaze cueing effect. In this study we applied the Diffusion Decision Model (DDM) to gaze and arrow cueing data for the first time in order to 1) better understand the cognitive processes underlying the gaze cueing effect, and 2) see whether these processes could be considered the same as those that underlie arrow cueing effects. To achieve these aims, we applied variants of the DDM to three preexisting gaze cueing data sets and one preexisting arrow cueing data set (n = 171, 139,001 trials total), using a combination of individual-level and hierarchical computational modelling techniques. At the group level, people were best described by an attentional orienting mechanism rather than higher-order decision bias or information processing mechanisms. However, we found evidence for individual differences such that not everyone was best described by an attentional orienting mechanism. Further, the same people who were best described by an attentional orienting mechanism for gaze cues tended not to be best described by that same mechanism for arrow cues, suggesting these cueing effects may induce different responses within the same people – although we interpreted this finding cautiously.