В статье представлены четыре этапа создания и развития теории пластин и оболочек, которые привели к разработке механизма расчета пространственных конструкций покрытий большепролетных зданий и сооружений на современном уровне. Приведены основные достижения специалистов в области строительной механики и проектирования зданий и сооружений в пределах каждого этапа. Отмечены наиболее важные научные результаты, которые повлияли на создание современных методов расчета и проектирования большепролетных конструкций покрытий. Даны примеры реализованных проектов большепролетных зданий и сооружений.The article presents the four stages of creation and development of the theory of plate and shell which led to the development of a mechanism of calculation of spatial structures of large span buildings and constructions on an advanced level. Each of the stages of the unique buildings calculation method development includes a description of the main achievements in the sphere of structural mechanics, the theory of elasticity and resistance of materials which became the basis for the modern theory of calculation of plates and shells. In the first stage the fundamentals of solid mechanics were developed; this is presented in works of such outstanding scientists as G. Galilei, J.-L. Lagrange, R. Hooke, L. Euler, Kirchhoff, A. Law etc. Development of the theory of plate and shell would be impossible without these works. But absence of such construction material as reinforced concrete did not enable engineers and architects to create a thin roof. Thickness of coverings was intuitively overstated to ensure durability of buildings. The second stage is interesting by formulation of the general theory of calculation of plate and shell and by transition from the working state analysis of structures to the limit state analysis. Beginning of use of reinforced concrete resulted in decrease of a roof thickness to the diameter of its base, compared to buildings made of stone and brick. The third stage is characterized by development of computational systems for calculation of strength, stability and oscillations of core and thin-walled spatial structures based on the finite element method (FEM). During this period a design of buildings and constructions with spans over 200 m with the use of metal was begun. Currently, or during the fourth stage, structures with the use of metal and synthetic materials for spans up to 300 meters are designed. Calculations of long-span buildings and structures are performed using FEM and taking into account different types of nonlinearity. Each stage selected from the history of construction is exemplified by completed projects, hereat characteristics of roofs indicating the applied construction material are given. Transition from natural stone to concrete, metal and synthetic materials in construction of large-span buildings is illustrated in the table. At the end of each stage the scientists’ and designers’ main achievements in the sphere of science, construction and engineering education are shown.