Global sensitivity analysis (GSA) estimates influence of design variables in the entire design domain on performance measures. Hence, using GSA, important design variables could be found for an engineering application with high dimension which require computationally expensive analyses. Then, similar engineering applications could use selected variables to carry out design process with smaller dimension and affordable computational cost. In this study, GSA has been carried out for the performance measures in design of stay vane and casing of reaction hydraulic turbines. Global sensitivity index method is used for GSA because it can fully capture the effect of interaction between the design variables. For efficiency, genetic aggregation surrogate models are constructed using the responses of computational fluid dynamic (CFD) analysis. Global sensitivity indices for the performance measures of stay vane and casing have been evaluated using the surrogate models. It is found that less than three design variables among 12 are effective in the design process of stay vane and casing in reaction hydraulic turbines.