In design, especially in preliminary design, the assumption of parameter accuracy is not justified, since the parameters here are inaccurate (uncertain), due to insufficient knowledge or lack of statistics, as well as the fact that design parameters are further implemented in the production with some tolerance. The application of deterministic optimization methods under conditions of parametric uncertainty can lead to unacceptable solutions even with slight variation in the parameters. Currently, to account for uncertainty of the parameters there are commonly used stochastic methods designed to account for aleatory uncertainty with a priori known distribution functions of random parameters. However, in the preliminary design, most of the parameters are not random variables with known distribution functions. The necessary information on the parameters is obtained from the experts. In this paper, we develop methods and algorithms for preliminary design in conditions of epistemic uncertainty arising from lack of knowledge and observation results, replenished by expert assessments. In the paper the problem of optimal design in the presence of input and design parameters with epistemic uncertainty is considered. The choice of Liu's uncertainty theory for solving the problems of preliminary design is justified. The model of uncertain design parameter and optimization model with uncertain design and input parameters are proposed. The task of optimal design of the propulsion system parameters of supersonic maneuverable airplane is solved using the proposed models. The results are compared with the solution using Monte Carlo method. The solution time using the proposed model is two orders of magnitude less.