In the work, methods of system mathematical modeling of surfaces of a simple and complex variable form of classes of congruent sections or unchangeable lines, as well as affine and projectively equivalent lines of frames, were studied and developed. The modeling is based on a scalar-parametric block-matrix form of representing surface equations, which is promising in computational computer geometry when solving software problems both when visualizing frames using machine graphics and when processing parts on CNC metal-cutting equipment. The work is recommended for students, undergraduates, graduate students, university teachers and researchers studying the possibilities of applying in practice the methods of engineering and machine graphics, descriptive and computational geometry.