The series expension of elastic Green's function of anisotropic cubic crystal is calculated and the expansion coefficients are given under the second order approximation. Applying the results to elastic dipole model, one obtains the expressions of elastic displacement field due to a symmetrical center and the interaction between two symmetrical centers. For strongly anisotropic cubic crystals such as K and Cu, it is surprising that the numerical results of the displacement field of the symmetrical center and the interaction between them are basically the same as those obtained by using lattice statics, which is based on the discrete native of the lattice, although the convergence is not very satisfactory. This seems to indicate that our analytical expression of the elastic Green's function leads to a simple and easy method, which can be used generally to describe some mechanical behaviour of cubic crystals correctly.