Abstract: The electromagnetic driven solid liner implosion is one of the high energy density physics (HEDP) experimental techniques. Because of the metal strength, there exists a threshold for driven pressure where plastic flow just begins. And the plastic work that will turn to the internal energy of the metal liner should decrease the kinetic energy of liner, which of course will affect the implosion of the solid liner. The critical current has been found via the elastic-plastic analysis of cylindrical symmetry issue. The zero-dimension (0D) simulation considering the effect of material strength has been developed, whose result is also compared with the simple model and experimental data separately. The result shows that the effect of material strength is negligible when the peak value of current is far larger than the critical current, while the effect is remarkable when the peak value is similar to the critical current.