The article presents the theoretical and methodological foundations of teaching a special course for students - architects on the application of geometric methods of shell formation in the design of modern high-rise buildings.The basic researches and publications which make a theoretical basis of teaching of a special course for architects with application of geometrical methods of formation of covers at designing of architecturally - constructive decisions of buildings are analyzed. The relevance of the use of curvilinear shapes in modern high-altitude architecture is substantiated, which is associated with the development of energy-efficient and bioclimatic design in high-rise buildings solved with extensive use of curvilinear surfaces. Directions for modeling changes in the formation of surfaces of high-rise buildings are identified. Methods of shaping are considered, which are based on geometric modeling of sets of lines, for given design conditions and obtaining by selecting from these sets the corresponding surfaces. An example of their application in the development of architectural - constructive solution of the high - rise complex is presented. As the experience of teaching has shown, the application of methods of geometric modeling in the development of architectural and structural solutions of buildings, develops in students new skills and design capabilities of architectural design. And the development of research on geometric modeling of surfaces, provides broad prospects for the modernization of the discipline in the future, as well as for the introduction of new areas of educational design.