The aim of the study is to identify the relevant aspects of numerical analysis of impact of projectiles with soft cores into a package composed of thin flexible plies located on the plastic backing. In order to illustrate the problem, normal impact of 7.62 mm TT projectile into an unclamped package comprising 36 plies of Dyneema SB71 supported on the plastic backing was selected. The problem was solved with the use of the finite element method (FEM) with the explicit integration scheme (central difference method) of motion equations in the matrix form. Based on the conducted numerical computations, it was revealed that obtaining the extreme deformations of a projectile soft core and the backing material in Lagrangian description requires employment of adaptive methods. The proposed R-adaptive method performs its role but must be used carefully due to the mass loss which may appear during calculations.