Abstract: With the algebratical calculation of matrix for general expression of stress-strain relationship of anisotropic linear elastic material, it is shown that the stress-strain behavior for this kind of material depends not only upon mechanical properties of material, but also upon geometric relation between the action direction of deviator stresses and the physical symmetric planes of material. It is demonstrated that global stress tensor causes not deformity, but also volume change. The special dilatency rule for anisotropic linear elastic material is shown more clearly with calculation of a simple example.