Abstract: Torseur theory is a mathematical tool tailored for mechanics, and it has advantages in describing the motion of rigid bodies. Based on the plain cross-sectional hypothesis in the strength of materials, the motion of a component's cross-section can be decomposed into displacement of the section center and rotation around the centroid. Therefore, the cross-section motion can be regarded as rigid body motion, and torseur theory can be used to describe the motion and force of components, providing a unified form from the mathematical perspective, and offering generality when dealing with combined deformation from the physical perspective. Moreover, the structural system force analysis described by the mathematical language turns the analysis of complex problems into formalized mathematical problems that can be solved based on the torseur operation rules. It is hoped that this research can provide new perspectives and ideas for the teaching of strength of materials in China.