The authors showed the possibility of using mathematical models based on artificial neural networks to determine the aerodynamic characteristics of helicopter profiles, as well as the ability to design new pro-files with specified aerodynamic characteristics. At the first stage of work, an approximation model based on a neural network of the multilayer perceptron type was created to determine the coefficients of lift, drag, and pitch moment of the profiles. This topology has a number of distinctive features and is well suited for solving such problems. Neural network training was conducted. As a training set, the calculated data of 3692 aerodynamic profiles were used. The accuracy of the approximation of aerodynamic characteristics was estimated. The expediency of using artificial neural networks to solve this class of problems was substantiated. At the second stage of work, to obtain the geometry of new profiles, a mathematical model was created on the basis of special classes of artificial replicative neural networks, which allowed us to significantly reduce the dimension of the space used to describe the surface of the aerodynamic profile and create a qualitatively new design system. Examples were given of using the system for creating profile families in the region of specified aerodynamic characteristics and limiting the maximum relative thickness of the profile