In the present work, we study the low velocity impact, both central and eccentric, on square and rectangular laminated composite plates with embedded shape memory alloy (SMA) wires, which are stitched on the top and bottom surfaces of the plate, by using the finite element method. In finite element methods (FEM) simulations, a super-elastic SMA constitutive model is implemented in Abaqus/Explict by using a user defined material subroutine to describe the behaviors of SMAs. The three-dimensional (3D) Hashin failure criterion is adopted to model the damage initiation of laminated composite plates. To model the delamination failure, a cohesive damage zone model is introduced in interface elements. A comprehensive parametric study has been carried out to analyze the effects of eccentricity for the case of square and rectangular laminated composite plates.