The decay rates of stresses and displacements due to self-equilibrated loads acting on the end of angle-ply laminated hollow cylinders are found by using the theory of three-dimensional elasticity. The study assumes that the periodic displacement and stress fields used decay away exponentially from the end load region. The use of a recursive and successive approximation method leads to an eigenmatrix whose eigenvalues represent the decay rates of the problem. By this approach, the composite cylinders may be composed of an arbitrary number of anisotropic layers, each of which may have different material properties, thicknesses and lamination profiles. The decay rates for anti-symmetrically laminated cylinders are found and presented. The effects of material properties, thickness and laminate profiles of cylinders upon the decay rates are investigated for typical anti-symmetric angle-ply laminated cylinders. (C) 2001 Elsevier Science Ltd. All rights reserved.