Incorporating uncertainties in the aeroelastic analysis increases the confidence levels of computational predictions and reduces the need for validation with experimental or flight test data. Helicopter rotor blades, which play a dominant role in the overall vehicle performance, are routinely made of composites. The material properties of composites are uncertain because of the variations in manufacturing process and other effects while in service, maintenance and storage. Though nominal values are listed, they are seldom accurate. In this thesis, the effect of uncertainty in composite material properties on the computational predictions of cross-sectional properties, natural frequencies, blade tip deflections, vibratory loads and aeroelastic stability of a four-bladed composite helicopter rotor is studied. The effect of material uncertainty is studied with the composite rotor blades modeled as components of soft-inplane as well as stiff-inplane hingeless helicopter rotors. Aeroelastic analysis based on finite elements in space and time is used to evaluate the helicopter rotor blade response in hover and forward flight. Uncertainty analysis is performed with direct Monte Carlo simulations based on a sufficient number of random samples of material properties. It is found that the cross-sectional stiffness parameters and natural frequencies of rotor blades show considerable scatter from their baseline predictions. The uncertainty impact on the rotating natural frequencies depends on the level of centrifugal stiffening of each mode. The propagation of material uncertainty into aeroelastic response causes large deviations from the baseline predictions. The magnitudes of 4/rev vibratory loads show deviations of 10 to 600 percent from their baseline predictions. The aeroelastic stability in hover and forward flight conditions also show considerable uncertainty in the predictions. In addition to the effects of material uncertainty, various factors influencing the propagation of material uncertainty are studied with the first-order based reliability methods. The numerical results have shown the need to consider the uncertainties in the helicopter aeroelastic analysis for reliable computational predictions. Uncertainty quantification using direct Monte Carlo simulation is accurate but computationally expensive. The application of response surface methodologies to reduce the computational cost of uncertainty analysis is studied. Response surface approximations of aeroelastic outputs are developed in terms of the composite material properties. Monte Carlo simulations are then performed using these computationally less expensive response surface models. The results of this study show that the metamodeling techniques can effectively reduce the computational cost of uncertainty analysis of composite rotor blades. In the last part of the thesis, an aeroelastic optimization method to minimize the vibration level is developed with due consideration to material uncertainty. Second-order polynomial response surfaces are used to approximate the objective function which smooths out the local minima or numerical noise in the design space. The aeroelastic optimization is carried out with the nominal values of composite material properties and the performance of final design is found to be optimum even for the perturbed values of material properties.