In engineering problems, the randomness and uncertainties are inherent and the scatter of structural parameters from their nominal ideal values is unavoidable. In Reliability Based Design Optimization (RBDO) and Robust Design Optimization (RDO) the uncertainties play a dominant role in the formulation of the structural optimization problem. In an RBDO problem additional non deterministic constraint functions are considered while an RDO formulation leads to designs with a state of robustness, so that their performance is the least sensitive to the variability of the uncertain variables. In the first part of this study a metamodel assisted RBDO methodology is examined for large scale structural systems. In the second part an RDO structural problem is considered. The task of robust design optimization of structures is formulated as a multi-criteria optimization problem, in which the design variables of the optimization problem, together with other design parameters such as the modulus of elasticity and the yield stress are considered as random variables with a mean value equal to their nominal value.