A multi-attribute robust design methodology is presented. This method can be applied where there are various technical constraints in design variables, multiple potentially conflicting design attributes, and uncontrollable noise variables. Two forms of technical constraints, soft and hard constraints, are considered in robust design settings. Specifically, this work presents procedures for integrating two types of design constraints seamlessly on the multiple design attributes, which is achieved through a development of multi-attribute utility formulation. The effectiveness of the overall procedures is tested with the aid of an I-Beam design problem, and results of sensitivity analysis are discussed.