Optical systems with variable optical characteristics (zoom lenses) find broader applications in practice nowadays and methods for their design are constantly developed and improved. Our work describes a methodics of the design of zoom lenses using the third order aberration theory. The proposed method makes possible to determine, which elements of the optical system can be only simple lenses and which elements must have more complicated design, e.g. doublets or triplets. It is also shown the method for optical system design that permits to calculate the radii of curvature and optical glass types for individual lenses.