Abstract This paper investigated the general instability of cylindrical shells in which the stiffeners formed spirals along the length and at an arbitrary angle with the axis. Two loading conditions were considered: uniform axial and lateral compressions and torsion. The stress-strain relations of the stiffeners were developed by rotation of the strain tensor. The buckling determinate was obtained by introducing into the equilibrium equations the admissible displacement functions consistent with the end constraints, thereby enforcing equilibrium by satisfying the characteristic equations. The buclking equations were programmed for a computer which rearched through a finite set of stress resultants for assigned values of spiral angle and modes and printed out the buckling load. The optimum structure weight of the stiffened shell was determined by iterating the design parameters at the required spiral angle so that the buckling load approached the applied load as a limit until the difference between these loads was within the design allowance.