Generative artificial intelligence (genAI) is becoming increasingly prevalent and capable in physics, particularly for programming-related tasks. How, then, does genAI affect students’ computational modeling? To answer this question, we conducted semi-structured interviews with 19 undergraduate students who had recently completed an open-ended computational assignment that encouraged the use of genAI, asking them how they used it. We then conducted a thematic analysis of these interviews using a framework for computational modeling in physics. We found that genAI significantly impacts several aspects of students’ computational modeling, such as the planning, implementing, and debugging of computational models. GenAI can also help students find resources and introduce them to new computational tools. Students reported finding genAI most helpful for their learning and productivity when they limited its use to small steps in the modeling process and consistently double-checked the formulas, explanations, and code it provided. Students also described challenges they faced due to an over-reliance on genAI, such as working from false model assumptions and not spending time learning the fundamentals of computational modeling, especially debugging. We discuss the implications of these findings for teaching, such as the need to teach students how to use genAI in a way that is helpful for their learning, which includes urging them to plan before they code. We also highlight the continued value of low-stakes assessment and teaching assistants for teaching computational modeling, as the task remains difficult even with the inclusion of genAI.