AbstractThe accuracy of stability analysis depends on the accuracy of both the element stiffness matrix and geometry stiffness matrix. Therefore, when carrying out the stability analysis of thin cylindrical shells using the finite element methods will require, firstly, a refined non‐conforming rectangular curved cylindrical shell element RCSR4 is proposed according to the refined non‐conforming FE method, in which both the C1 and C0 weak continuity conditions are satisfied and as a result, can ensure the convergence of computation. At the same time, a refined geometrical stiffness matrix is introduced to replace the standard consistent geometrical stiffness matrix. Simple expressions of the refined constant strain matrices with adjustable constants are introduced with respect to the weak continuity conditions. Numerical examples are presented to show that the present method can indeed improve the performance and the accuracy in stability analysis. Copyright © 2001 John Wiley & Sons, Ltd.