Software modeling is an essential practice in software engineering, requiring the application of both abstract thinking and systems thinking. Despite its importance, there is limited empirical research on how these cognitive skills are enacted during the modeling process. This study investigates how undergraduate students apply abstract and systems thinking while constructing software models using Unified Modeling Language (UML). Employing a case study approach with think-aloud protocols, the research is framed through the lens of epistemic forms and games to analyze student reasoning. Six students who had completed a second-year systems analysis and design course participated in the study. Thematic analysis of their modeling sessions revealed how abstract and systems thinking were enacted through structural, functional, and process-oriented epistemic games. Two distinct modeling sequences—structural-before-behavioral and behavioral-before-structural—were identified, each associated with different cognitive strategies. Chronological visualizations were developed to illustrate these modeling paths. Key contributions of this study include a novel integration of epistemic games into modeling analysis, a detailed characterization of student modeling behavior, and actionable recommendations for instructional scaffolds to support the development of modeling proficiency in computing education.