The article discusses the issues of stability of single-layer cylindrical rod roofs and establishes the suitability of the theory of thin solid shells for similar-shaped core structures. An analysis of the factors was carried out to determine the magnitude of the critical load and the need to take into account the parameter characterizing the change in the geometry of the structure along the arc of the circle was proved. The values and ratio of flexural and membrane stiffness are obtained depending on the possible number of half-waves of the shape of the loss of stability, and a pattern for determining the critical load is established.

Keywords: cylindrical rod roofs, stability, critical load, stiffness, number of half-waves