This work is focused on the strong deformation motion mechanism of multi-layer metallic materials under extreme pressure conditions accompanied by a strong impact effect between the projectile composed of multi-layer metallic materials and the steel barrel of the launcher itself. Here, this transient engraving process of the projectile with complicated stress-strain based on a new type of structure and propulsion pattern is firstly studied by proposing a new physical and mathematical model with a coupling of dynamical equations and two-stage combustion ballistic equations. Comparisons of engraving distance of computational results are done with experimental studies, and a reasonable match has been obtained in these comparisons. Further, the thickness effect of the metal jacket of the projectile on the engraving stress and deformation level is analyzed to obtain universal engraving resistance equations. The results have also shown that the projectile's whole transient deformation motion process in the launcher can be divided into three periods due to the initial slide impact effect under the first-stage propellant gas and the later propelling effect as the second-stage propellant is ignited. However, the engraving durations are all less than 0.7ms with different levels of elastic-plastic deformations between multi-layer metallic materials for different conditions.