Researchers in physics education have advocated both for including modeling in science classrooms as well as promoting student engagement with sensemaking. These two processes facilitate the generation of new knowledge by connecting to one's existing ideas. Despite being two distinct processes, modeling is often described as sensemaking of the physical world. In the current work, we provide an explicit, framework-based analysis of the intertwining between modeling and sensemaking by analyzing thinkaloud interviews of two students solving a physics problem. While one student completes the task, the other abandons their approach. The case studies reveal that particular aspects of modeling and sensemaking processes co-occur. For instance, the priming on the 'given' information from the problem statement constituted the students' engagement with their mental models, and their attempts to resolve inconsistencies in understanding involved the use of external representations. We find that barriers experienced in modeling can inhibit students' sustained sensemaking. These results suggest ways for future research to support students' sensemaking in physics by promoting modeling practices.