The method of designing elements of the surfaces' frames based on array of points is suggested in the work. Elements of frames are contours that are received via interpolation of sets of points, which are selected from the initial array of points. The algorithms have been developed for design plane and spatial contours that represent the curves with specified geometrical properties with prescribed accuracy. Formed contours are used as elements of «Profile» and «Guide Curves» at forming the model of surface by means of function of «Lofted Surface» in CAD system. Using the method of designing elements of frames of the surfaces is actual for modeling of surfaces of technical items that function-interact with the environment. The developed method was proven while modelling functional surfaces that bound an impeller blade channel of a turbine compressor.