This paper presents a cognitive model that simulates reliance on automation using a line-tracing task similar to driving where an operator has to track a moving line with a circle by pressing keys on a keyboard (manual control) or rely on automation (auto control). An operator can switch between auto and manual control during the task. The success proba- bilities of each control mode were systematically varied. An ACT-R model to perform this task was constructed by repre- senting reliance on the automation as production. The model performs this task through productions that manage the per- ceptual/motor modules. The utility values of these productions are updated based on the rewards in every screen update. We also introduce a meta-level monitoring the internal state of the model. A preliminary run of this model simulated the overall trends of the behavioral data, suggesting some validity of the assumptions made in our model.