Deformations and stresses in hybrid shape memory alloy plates subjected to low-velocity impact are considered. Shape memory alloy fibers embedded in resin sleeves and located at the middle plane of the plate can be an effective tool for the reduction of deformations and the control of damage. The desirable effect can be achieved by activating the fibers, i.e., through a constrained reverse transformation. In the examples considered in the paper, transverse deflections were reduced to approximately one-third of the deflections of identical plates without shape memory alloy fibers. Although the benefits to the stresses were less impressive, they were still significant. The accuracy of the closed-form solution presented in the paper is limited only by a number of terms in the series that represent deformations. Numerical analysis reflected a good convergence of the solution.