Arteries are modelled, within the framework of non-linear elasticity, as incompressible two-layer cylindrical structures that are residually stressed through differential growth. These structures are loaded by an axial force, internal pressure and have non-linear, anisotropic, hyperelastic response to stresses. Parameters for this model are directly related to experimental observations. The possible role of axial residual stress in regulating stress in arteries and preventing buckling instabilities is investigated. It is shown that axial residual stress lowers the critical internal pressure leading to buckling and that a reduction of axial loading may lead to a buckling instability which may eventually lead to arterial tortusity. © 2010 The Author. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.