The paper presents the test results for the three-layered structures with lightweight lattice cores made by three-dimensional printing using selective laser sintering technology with polyamide. The used core structures correspond to the so-called pantographic mechanical metamaterials, in which two systems of parallel beams are spaced apart by a small distance and connected to each other by transverse pivots at the intersections. For such materials, it is known that to describe their equivalent mechanical characteristics, it is necessary to use non-classical models of the theory of elasticity taking into account the nonlocal nature of the deformations of the structure of the material under loading. In this paper, we consider three options for transverse connections in the structure of the metamaterial, in which the transverse pivots provide the transition of both forces and moments (rigid joints), only forces (pinned joints) or are simply absent. Such cores are compared with a conventional lattice core, in which the intersecting beams form a rigidly connected system such as a flat frame. The fabricated samples were tested for the impact resistance according to the double-support shock bending scheme using pendulum impact testing machine. It has been established that with the same cross-sectional dimensions of the rods in the core, the samples with pantographic core with rigid transverse joints have the greatest bload earing capacity under impact. However, specimens with pinned joints exhibit unusual fracture mechanisms in which the damage zone is greatest and damage develops with the formation of many small fragments that impede the passage of the projectile through the structure and increase its specific energy absorption, which makes such core options potentially promising for creating energy absorbing structures.