Abstract: Assuming that transversely isotropic material with its plane of isotropy parallel to the x-y plane, the equilibrum equations are E_{iklm u1,km}=0 (1) E_jklm is very complicated for transversely is otropic materials.In order to write out fundamental solution of equation(1),we introduce potential functions Φ,Ψ and φ. Using the relation between u_i and Φ, ψ, φ, we can take fundamental solution of equation(1),Substituting fundamental solution into boundary integral, the integral equation can be solved by discretisation procedure.