A solution strategy for designing flexible process flow sheets with a large number of uncertain parameters is presented. The basic mathematical formulation is a two-stage stochastic program transformed into its multi-scenario deterministic equivalent. The main feature of the proposed approach is a tremendous reduction in scenarios to a smaller number of those critical ones. This reduction is achieved through simple sensitivity analyses that identify those uncertain parameters that are critical for feasibility and those that are involved in a stochastic approximation of the objective value. Through the application of this strategy, it is possible to solve the problems with several tens or even hundred uncertain parameters, assuming weak interactions between them. Feasible designs are obtained for a fixed degree of flexibility, while the expected objective function is approximated fairly well. The strategy is applied to two flow sheet examples. (c) 2013 American Institute of Chemical Engineers AIChE J, 59: 2862-2871, 2013