Stope design optimization defines mineable three-dimensional material volumes to be extracted from a mineral deposit, aiming to maximize cashflows subject to geotechnical, geological, and operational constraints related to the selected stoping underground mining method. The current industry practice considers a stope design as the input into subsequent optimization steps: development network layout and production scheduling, leading to life-of-mine planning and related forecasts. Available stope layout optimization methods are deterministic and are based on conventionally estimated orebody models; thus, they fail to consider the geological uncertainty and variability that affects the stope locations and sizes. A two-stage stochastic integer programming formulation for stope design optimization is proposed. The model integrates grade uncertainty, quantified through geostatistical simulations of a mineral deposit, level allocation, variable stope sizes, pillar requirements, development costs and slope stability parameters for different geotechnical zones. An application at an underground gold mine employing sublevel open stoping is presented. Results highlight how the integration of grade uncertainty and variability define a risk-resilient stope design, capturing the upside potential in terms of metal recovered.