In this thesis, low-velocity impact (LVI) on the Carbon-fiber reinforced polymer (CFRP) sandwich plate with re-entrant auxetic core is modeled by theoretical analysis. The Zig-Zag theory is used to write the displacement field of the sandwich panel. A nonlinear Hertz contact model is applied to express the impact force between impactor and upper face sheet of the sandwich panel. The equivalent mechanical properties of the re-entrant auxetic core unit cell is provided by using the Gibson's equations. Finally, by using the energy method and the polynomial shape functions related to the geometric boundary conditions in the Ritz method, the impact motion equations are extracted. The influences of the unit cell thickness, the number of layers of unit cell along the thickness of the plate, the impactor radius, and the impactor initial velocity on the LVI response of CFRP sandwich plate with re-entrant auxetic core are investigated in detail. Among the most important results, it can be pointed out that with the increase in the thickness of the core unit cell, the maximum contact force and the impactor residual velocity increase, but the peak displacements of the plate and the impactor decrease.