This paper offers a method for weight optimization of multilayer fiber composite PLATES under the action of lateral loadings. The objective is to design a fiber composite plate of minimum thickness which can sustain multiple static loadings applied normal to its surface without exhibiting failure of any kind in anyone of its layers. In this investigation, fiber orientation angles are treated as discrete variables, which can vary only by pre-assigned increments. The thicknesses of layers are treated as continuous variables. The optimization procedure is based on a two stage strategy; in the first of which only the angles of layers, and in the second, the layer thicknesses are treated as variables. The two distinct stages that are executed separately in every iteration, is capable of consecutively choosing new layers (as identified by their orientation angles) of minimum possible thicknesses to be added to the set of layers in the laminate, provided those orientation angles prove to be the most useful. Reduction of the total thickness is treated as the criterion of usefulness of a new layer to be added to the set already at hand. The priorities exercised in the choice of new layers for inclusion in the set, allow an optimal state of stacking order to be achieved. At the same time, minimum total thickness criterion for acceptance of a new layer would exclude all unnecessary layers from the set. The end result would be a laminate of minimum total thickness whose layers appear in their proper position in the stack and with proper angle orientations. The maximum number of layers required in a set is arrived at by the rejection of all possible candidate angles, signaling the end of the optimization process. Thus the least total thickness, corresponding to the order in which layers of different angle orientation should be stacked, as the end result is achieved with no limitations imposed on the variation of orientation angles. Several examples are shown to demonstrate the operation of the algorithm.