Physics education researchers have advocated for modeling and sensemaking to be part of students' science learning environments as the two processes lead to generation of new knowledge by connecting 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 operationalizing the Denotative Function (DF), Demonstration (D), and Inferential Function (IF) -the DFDIF account of modeling -, and the Sensemaking Epistemic Game in the context of physics problem solving. The data involves two case studies, one involving participant's successful completion of the task and the other in which the participant aborts his attempt at the solution. Qualitative analysis of the participants' problem-solving moves reveals that modeling -construction of mental models and engagement with the DFDIF components -to entail navigation through the stages of the Sensemaking Epistemic Game. We also observe co-occurrence of construction of mental models, engagement with modeling's Demonstration and Inferential Function with the Assembling of a Knowledge Framework, Generation of an Explanation, and Resolution stages of the Sensemaking Epistemic Game respectively. Additionally, the second case study reveals that barriers experienced in modeling a context can inhibit participants' sustained sensemaking. Limitations of the current work and implications for future explorations are discussed.