The paper presents an approach to the problem of optimum design of composite plates subjected to low velocity impact. The deflections and stresses are reduced by employing prestrained shape memory alloy (SMA) fibers which are in the martensitic phase when embedded within the plate. At an elevated temperature, the SMA fibers transform into the austenitic phase and tend to contract. However, due to a constraint, the contraction is either completely prevented or reduced resulting in significant tensile recovery stresses. This tension reduces deformations and stresses in the plate subjected to low-velocity impact. The solution in the paper addresses an impact of cross-ply plates with SMA fibers embedded within the layers oriented in both directions. An approach to optimization considered in the paper involves variations of the volume fractions of SMA fibers in each direction subject to a constraint on the total volume of the shape memory alloy. It is shown that an application of SMA fibers can significantly reduce deflections and stresses. A further benefit can be achieved by an optimization of a distribution of volume fractions of SMA fibers between the layers.