In order to accurately describe the shape of behind-armor debris cloud from vertical penetration of a finite-thickness target plate by an explosively formed projectile（EFP），the dimensional analysis and the theory of orthogonal design were used as bases in this work. The effect of EFP molding parameters and the material parameters of projectile and target plate on the shape of behind-armor debris cloud were studied using SPH algorithm in AUTODYN software. A mathematical description model of the debris cloud shape behind armor from vertical penetration by an EFP was established. The shape parameter of major semi-axis of behind-armor debris cloud from a vertical EFP penetration was calculated using that model and compared with the simulated and related experimental results. It is proved that the error between the calculated major semi-axis result of debris cloud by that model and the related experimental result is controlled within 3%，and the shape of behind-armor debris cloud formed by an vertical EFP penetration can be described accurately with this model.