A thick shell model is presented that takes into consideration the most important material and geometrical issues of arterial wall mechanics. Like its conventional counterparts, it uses a fixed and small number of unknowns. Its remarkable success is however based on the incorporation into its displacement field of exact elasticity solutions available for corresponding cylindrical tubes of infinite extent. With this incorporation, the proposed 2D model and 3D elasticity yield identical stress distributions, at least within small deformations and linearly elastic material regimes. Its relevance to the theme of this conference stems from its ability to account further for important characteristics met in arterial wall mechanics (e.g., layered structure, non-linear elastic behaviour, large deformations, pre-stress, temperature effects). Apart a small number of relatively simple relevant boundary value problems that might be tackled analytically, exploitation of its full potential is achievable only with the use of modern methods of numerical analysis and computational mechanics.