Computational thinking (CT) is a critical skill needed for STEM professionals and educational interventions that emphasize CT are needed. In engineering, one potential pedagogical tool to build CT is modeling, an essential skill for engineering students where they apply their scientific knowledge to real-world problems involving planning, building, evaluating, and reflecting on created systems to simulate the real world. However, in-depth studies of how modeling is done in the class in relation to CT are limited. We used a case study methodology to evaluate a model-planning activity in a final-year undergraduate engineering classroom to elicit CT practices in students as they planned their modeling approach. Thematic analysis was used on student artifacts to triangulate and identify diverse ways that students used CT practices. We find that model-planning activities are useful for students to practice many aspects of CT, such as abstraction, algorithmic thinking, and generalization. We report implications for instructors wanting to implement model-planning activities into their classrooms.