Spatial deformation of the system, composed of the rod elements, is considered. A mathematical model is based on the finite element method. Each finite element is associated with a moving local coordinate system. Displacements and rotations of local systems are taken into account rigorously. Shape functions are obtained from the solution of the homogeneous boundary value problem using local system variables. Asymptotic approach is used for obtaining the basic deformation relations in the quadratic approximation from the general relations of nonlinear elasticity.