Abstract: Irreducible parts of elastic compliance (modulus)tensor are presented. It is shown that Viogt average (polycrystalline) elastic constant can be obtained from the scalar parts of the elastic constant irreducible parts. It is also shown that the volumetric compressibitly is directly related to the first irreducible scalar part of the elastic compliance tensor and this relation holds for all symmetries of the linearly anisotropy materials. Norm concept of Cartesian Tensor is given. The norm of a Cartesian tensor is used as a criterion for representing and comparing the overall effect of a certain property of the same or different symmetry. The norm of elastic compliance tensor and the norms of the Irreducible parts for different materials are calculated. The relation of the scalar parts norm and the other parts norms and the anisotropy of the material are presented.