This paper presents a new geotechnical design concept, called Robust Geotechnical Design (RGD). The new design methodology seeks to achieve design robustness and economics, in addition to meeting safety requirements. Here, a design is considered robust if the variation in the system response (i.e., failure probability) is insensitive to the statistical characterization of noise factors, such as uncertain geotechnical parameters. It can be shown that when safety requirements are met, cost and robustness are conflicting objectives with a trade-off, meaning that a single best design may be unattainable. In such a case, a multi-objective optimization considering cost and robustness can be performed to obtain a suite of best designs within the solution space in which safety is guaranteed. To this end, the suite of best designs forms the Pareto Front, which is a useful tool to aid in the design decision making within the RGD methodology. The new design methodology is illustrated with examples of spread foundation designs and rock slope designs, through which the significance of the RGD methodology is demonstrated.