The article presents the main algorithm for obtaining new forms of linear quasi-polyhedrons is stated, the main layout diagrams of their shaping are given. The resulting forms of various types of new quasi-polyhedrons from the parts of hyperbolic paraboloid are shown as an effective artistic-aesthetic and technical alternative to the well-known flat-sided polyhedrons and curvilinear / hyperbolic quasi-polyhedrons. The forms obtained by the author differ significantly from the prototypes in appearance and technical qualities, which allows us to speak about the expansion of their effective functional range in different fields of modern design.