The net system connected by an arbitrary number of rods with arbitrary topologic construction was discussed in this paper. Based on the Gauss’s principle of least constraint, the approach of dynamic modeling for the net system of rods was proposed. The background of the study selects the large deployable structures composed of trusses and meshes in the astronautic engineering. The Kirchhoff′s model of elastic rod was applied to describe the motion of rods, the large deformation of which can be unlimited. The general form of the constraint function for the net system was derived, and the geometric constraint conditions of rods exerted by connected joints were given. The related dynamic model can be used to determine the motion of the net system by the variation method directly without dynamical differential equations. The real motion of the system was obtained through seeking the minimal value of constraint function from different possible motions, in which the joint constraint conditions can be satisfied in advance. As a special case when the rods are flexible enough, neglecting the bending and torsional rigidities and considering the axial deformations, the net system of rods was transferred to a net system connected by flexible cables. Moreover, a net system composed of five rods was taken as an example in the explanation of the modeling process.