Abstract: A static model for super-thin elastic rod is described. The rod is treated as a process of a cross section moving along its axial line at a constant velocity, assuming a plane cross-section. The geometry of deformation of the rod section is discussed and differences between the Kirchhoff model and the Cosserat model are analyzed based on the definitions of strain vector at the center and curvature-twisting vector of the section. According to the equilibrium condition of a differential segment of the rod, a differential equilibrium equation of Cosserat model is derived. Closed form constitutive equations on principal vector and principal moment of forces acted on the section are given. The constraints subjected to the ends of rod are discussed and boundary conditions for the rod are given. It is concluded that equilibrium of the rod is a statically indeterminate problem.

Key words: super-thin elastic rod, Kirchhoff model, Cosserat model, differential equilibrium equation, boundary condition