Objective: The aim of this article is to develop a formal model of conflict detection performance. Background: Our model assumes that participants iteratively sample evidence regarding the state of the world and accumulate it over time. A decision is made when the evidence reaches a threshold that changes over time in response to the increasing urgency of the task. Method: Two experiments were conducted to examine the effects of conflict geometry and timing on response proportions and response time. Results: The model is able to predict the observed pattern of response times, including a nonmonotonic relationship between distance at point of closest approach and response time, as well as effects of angle of approach and relative velocity. Conclusion: The results demonstrate that evidence accumulation models provide a good account of performance on a conflict detection task. Application: Evidence accumulation models are a form of dynamic signal detection theory, allowing for the analysis of response times as well as response proportions, and can be used for simulating human performance on dynamic decision tasks.