Abstract: The classical framework of mechanics of materials is based on the assumption of linear elasticity and small deformations. By simplifying geometric relationships (ignoring the impact of deformations on equilibrium equations) and physical relationships (assuming a linear stress-strain relationship), it provides an efficient and concise theoretical tool. However, nonlinear problems are inevitably encountered in engineering practice. Taking two competition questions from the National Zhou Peiyuan Mechanics Competition for College Students as specific case studies, this paper analyzes two types of nonlinear problems in mechanics of materials—geometric nonlinearity and physical nonlinearity—and identifies errors in the provided solutions or problem designs.