The book reflects the modern theory and practice of calculating the stability of thin shells. Nonlinear and linear shell theory and methods of their research on stability are systematically presented. Generalized and systematized well-known theoretical and experimental studies. Unlike the known books containing either classical or nonlinear interpretation of the stability of shells, the results related to taking into account the actual nature of the initial stress state of the shells. are presented. Research of this kind has the greatest practical value. The book presents algorithms for calculating the stability of shells on a computer and the results of studies brought to formulas and graphs convenient for practical use.