Abstract: Torsion of prismatic bars is one of the core topics in mechanics of materials and elasticity courses, and it also serves as a representative loading case for helping students understand stress functions, governing equations, and boundary conditions. To address the limitations of traditional instruction—including complicated analytical derivations, high operational cost of numerical modeling, time-consuming in-class theoretical deduction, difficulty in achieving real-time visualization, and limited extensibility of teaching content—this study introduces physics-informed neural networks (PINN) into the teaching practice of Saint-Venant torsion and establishes a “theory–intelligence” collaborative teaching framework. A circular cross-section benchmark case is first used to illustrate the PINN modeling procedure, after which the method is extended to non-circular cross-sections represented by elliptical and rectangular domains. The prediction accuracy and visualization performance are validated against analytical solutions and reference numerical solutions, respectively. The results demonstrate that PINNs can accurately reconstruct the Prandtl stress function and the shear stress distribution without mesh generation, while enabling millisecond-level full-field inference. This makes the proposed approach suitable for real-time interactive demonstrations in the classroom as well as students’ self-directed exploration outside class. Moreover, it helps deepen students’ understanding of the underlying physical mechanisms, cultivate scientific thinking and innovation capability for complex engineering problems, and stimulate interest in exploring emerging technologies.