Student satisfaction is widely used as an important indicator of higher education quality and teaching effectiveness. However, existing research has largely been developed within general higher education contexts and offers limited explanation of how student satisfaction is formed in practice-intensive performing arts programmes. Undergraduate musical theatre education, which combines embodied training, cross-skill integration, rehearsal practice, and translation into stage performance, provides a valuable context for reexamining student satisfaction in performing arts education. Therefore, this study aims to explore how student satisfaction is formed in undergraduate musical theatre education and to develop a process-oriented model explaining its underlying mechanisms. Drawing on a procedural grounded theory approach, this study conducted semi-structured interviews with 15 students and recent graduates from five Chinese institutions with relatively well-established undergraduate musical theatre programmes. The interview data were analysed through open coding, axial coding, and selective coding. The analysis generated 36 open-coding categories, which were further organized into 12 main categories: teaching conditions, curriculum and time structure, performance support, training continuity, pedagogy and feedback, integrated training quality, creative and humanistic development, practice and external linkages, perceived capability development, perceived career readiness, commitment and alignment, and overall satisfaction. Based on these findings, the study developed a training-continuity model of student satisfaction. The results indicate that structural conditions shape students' learning experiences by enabling or disrupting training continuity, while pedagogical transformation mechanisms further influence perceived capability development and perceived career readiness. These perceptions contribute to overall satisfaction by strengthening professional identification, perceived assessment fairness, and willingness to remain engaged. This study shifts the understanding of student satisfaction from a service-quality perspective commonly used in general higher education to a training-system perspective suited to practice-intensive performing arts education. It identifies training continuity as a central mechanism linking structural conditions, pedagogical processes, and outcome perceptions, and provides practical implications for improving undergraduate musical theatre curricula.