Abstract: The core of cross-section is an important concept in the design of the columnar structure of concrete non-tensile materials under compression in the field of civil engineering. In order to deepen students' understanding of the concept of the core of cross-section in the course of material mechanics, it first developed a programing code with MATLAB to calulate the core of cross-section. The concrete numerical examples help students to understand the concept more easily. Then the convexity of the core of the cross-section was discussed. The convexity of the core of the section is explained by the static equivalence principle and the superposition principle from the perspective of mechanics; the convexity is proved mathematically by the neutral axis equation and the definition of convex set. The teaching process is helpful in cultivating students thinking skills.