Abstract: in this paper, based on theory of internal state variables in continuum mechanics,a fibre bundle model of material states are presented. First of all, the states of material aredivided into the internal microstructural states and the external deformation states. Assumingthat the plastic deformation of material can be given by the internal states of material and theirevolution laws, a principal fibre bundle structure and the correspondent relationships between thegeometrical characterization and the mechanic...