Abstract: Based on the Hamilton principle, a coupled motion equationof stretching metallic shaped-charge jet is presented to study the effectsof yield strength, shear, strain rate, viscosity, surface tension force andvelocity gradient on the jet instability, and the results arequantitatively discussed. The value range ofnon-dimensional \lambda _m \dot \varepsilon _0 was obtained toillustrate the product of the wavelength in unstablest solution and initialstrain rate. Furthermore, the criterion and approximate theoretical formulaof jet breakup time are presented. The theoretical results were in fairlygood agreement with the jet experimental data and those from the methoddeveloped by Chou and Carleone.