A topical task of developing optimization algorithms for the parametric synthesis of the supersonic passenger transport (SST) aerodynamic configuration under epistemic uncertainty (lack of sufficient knowledge to determine input parameters of the aerodynamic calculation) is addressed in the paper. These algorithms are proposed to be used when the values of the initial calculation parameters are set by experts due to the lack of accurate or statistical data about the design object that is a fuzzy formulation. To solve such a problem, Liu's uncertainty theory was chosen, which provides computational efficiency when performing optimization calculations and allows using existing deterministic algorithms such as Black-Box Models when calculating objective and restriction functions. Solving the problem of parametric synthesis of the SST aerodynamic configuration in a fuzzy formulation, we propose the optimization models, the schemes for designing and using algorithms based on these models and present the results of computational studies. Proposed method application is considered to a generalized SST.