The development and comparative analysis of optimization models for the conceptual design of aircraft with nondeterministic input parameters are addressed using probability and uncertainty theories. Probability distribution functions describing the uncertainty of initial data are typically unknown at the stage of conceptual design. In this case, a possible approach to the construction of models with nondeterministic parameters is based on probability theory and frequency interpretations of uncertainties. To develop alternative optimization models designed to work with expert information, we chose uncertainty theory, which relies on principles similar to the generally accepted Kolmogorov axiomatics and allows for a reduction in computational costs by eliminating the requirement for measure additivity. The study focuses on the synthesis of reliable design solutions, which is of particular relevance in engineering practice. By formalizing the nondeterminism of the initial data using uncertain and random parameters, two sets of two-criteria models were developed that optimize the quantile and critical values of the objective functions. The objective functions are part of a computational algorithm that integrates aircraft parameter calculation models at the conceptual design stage. The results of a comparative analysis are presented, including computational costs and a comparison of Pareto fronts for different levels of uncertainty and reliability requirements.