The response of elliptical composite cylindrical shells under torsion is studied. The torsional condition is developed by rotating one end of the cylinder relative to the other. Prebuckling, buckling, and postbuckling responses are examined, and material failure is considered. Four elliptical cross sections, defined by their aspect ratio, the ratio of minor to major radii, are considered: 1.00 (circular), 0.85, 0.70, and 0.55. Two overall cylinder sizes are studied; a small size with a radius and length for the circular cylinder of 4.28 in. and 12.85 in., respectively, and a large size with radii and lengths five times larger, and thicknesses two times larger than the small cylinders. The radii of the elliptical cylinders are determined so the circumference is the same for all cylinders of a given size. For each elliptical cylinder, two lengths are considered. One length is equal to the length of the circular cylinder, and the other length has a sensitivity of the buckling twist to changes in the length-to-radius ratio the same as the circular cylinder. A quasi-isotropic lamination sequence of a medium-modulus graphite-epoxy composite material is assumed. The STAGS finite element code is used to obtain numerical results. The geometrically-nonlinear static and transient, eigenvalue, and progressive failure analysis options in the code are employed. Generally, the buckling twist and resulting torque decrease with decreasing aspect ratio. Due to material anisotropy, the buckling values are generally smaller for a negative twist than a positive twist. Relative to the buckling torque, cylinders with aspect ratios of 1.00 and 0.85 show little or no increase in capacity in the postbuckling range, while cylinders with aspect ratios of 0.70 and 0.55 show an increase. Postbuckling shapes are characterized by wave-like deformations, with ridges and valleys forming a helical pattern due to the nature of loading. The amplitudes of the deformations are dependent on cross-sectional geometry. Some elliptical cylinders develop wave-like deformations prior to buckling. Instabilities in the postbuckling range result in shape changes and loss of torque capacity. Material failure occurs on ridges and in valleys. Cylinder size and cross-sectional geometry influence the initiation and progression of failure.