In this paper, on the basis of the constitutive relation theory which includes inner variables, with the general explicit description of incremental strain thermal-plastic constitutive relations and the specific incremental thermal-plastic constitutive relations, combining the simulation of X ray load and the tube responsing problem which is greatly important in practice, the self-contained equation group about the stress wave in the flexible material_steel composite shell problem is developed. Numerical simulations are carried out with the presented constitutive relations for explosive-filled sphere fracture problem and the results are analyzed.  The thickness of explosive and flexible material that influences the load of the interface is discussed emphatically.