In this paper a theory of equilibrium and stability of elastic thin-walled cylinders is proposed. The theory is based on the following assumptions: 1) The cross section of the cylinder is uncleformable. 2) The cylinder is under a system of initial stresses σz0=- P0/F-My0/Ixx x + Mx0/Iyyy. This theory may be regarded as a generalization of V. Z. Vlasoff's theory of stability of thin-walled rods, and includes the theory of Karman-Chien and Adaduroff as a special case. For cases of simply supported cylinders and cantilever cylinders, a method of solution using trigonometric series is proposed which is much simpler than the methods used by Karman-Chien and Adaduroff.