Abstract: The classical framework of Mechanics of Materials is centered on the assumption of linear elasticity and small deformations. By simplifying geometric relationships (ignoring the impact of deformations on equilibrium equations) and physical relationships (where the stress-strain relationship is linear), it provides an efficient and concise theoretical tool. However, nonlinear problems are inevitably encountered in engineering practice. Taking two competition questions from the Zhou Peiyuan College Student Mechanics Competition as specific research carriers, this paper analyzes two types of nonlinear problems in Mechanics of Materials, including geometric nonlinearity and physical nonlinearity, and points out the errors in the answers or question designs of these competition questions.