The materials used in aerospace structures such as antenna, satellites and missiles should have such features as low density, high stiffness, low coefficients of thermal and moisture expansions simultaneously. Fiber reinforced polymer composite materials can satisfy these requirements with an appropriate stacking sequence using optimization methods and hence dimensionally stable composites are obtained. In this thesis, two different materials carbon/epoxy and E-glass/epoxy composites are considered. Both materials have been used for optimization, stress and failure analysis. However, only for E-glass/epoxy, experimental studies have been performed including determination of stiffness, strength characteristics, Poisson’s ratio, fiber volume fraction, glass transition temperature (Tg) and coefficient of thermal expansion (CTE). The objective of optimization part is to design the stacking sequence of the carbon/epoxy and E-glass/epoxy laminated composites having low CTE and high elastic moduli. In design process, multi-objective genetic algorithm optimization of the carbon/epoxy composite plates are verified by single-objective optimization approach by using the Genetic Algorithm (GA), Generalized Pattern Search (GPS) and Simulated Annealing (SA) algorithms. MATLAB Optimization Toolbox is used to obtain Pareto-optimal designs and global optimum points for different model problems. Stress and strain distributions are presented through the thickness of the laminates subjected to mechanical, thermal, and hygral loadings. Stress analysis results showed that effect of mechanical loads dominate to hygral and thermal loads. All the stochastic search methods carried out in the present thesis have produced almost the same results with different stacking sequences.