The increasing use of the laminated composite plates in the construction of mechanical, aerospace, marine, and automotive structures has made the design of these laminates an important research topic. One of the most important reasons for using laminated composite materials in these applications is to reduce the structural weight. Consequently, the main objective of this thesis is to find the minimum weight design of the laminated plates under the application of dynamic loads and subject to different flexibility and strength constraints. The common objective in the optimal design of laminated composite plates is to determine layer orientation, layer thicknesses, or number of layers to obtain the minimum weight of the structure and to satisfy the imposed constraints. In this work the ply thicknesses are taken as a continuous design variables. The optimal ply orientation and the optimal lamination scheme are determined through a parametric study according to the boundary conditions of the problem and the aspect ratio of the plate.