Abstract: In developing assumed stress hybrid elements, a major obstacle is how to select the rational element stress patterns. It is very difficult to find the equilibrating stress trial functions for axisymmetric problems. The early works in this aspect were in an experience state. In recent years, a new way for formulation of hybrid elements was suggested by Pian et al and it has become a basis of determining element stress patterns. In the derivation, however, some perturbation treatments are usually needed and the corresponding axisymmetric hybrid elements are not universal to regular and irregular meshes. In the present paper the optimizing priciple of hybrid finite elements is applied to axisymmetric analysis so the problems mentioned above are solved comletely. The optimized hybrid model shows a superior numerical behavior, i. e.1. It passed the patch test. 2. In comparision with 4-node axisymmetric displacement element, the present method yields more ideal results for both stresses and displacements and is espacially suitable for nearly incompressible materials without any locking phenomena. 3. The optimized hybrid element is universal for any types of meshes. 4. No false shears, no zero energy modes. ?. , ?-