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In the study of elastodynamic problems of inhomcgeneities, a kind of integrals of the type exp (iαR)/Rdv’ are frequently presented. In this paper the problems caused in evaluating Φ-integrals by Taylorseries expansions are discussed. Further the formulas of evaluating the Φ-integrals are obtained by using potential theory. The recursion formulas for the potential integrals are given. The result play an importent part not only in the elastodynamics problems of inhomcgeneities but also in the integration of inhomogeneous Helmholtzequation associated with the problems of wave phenomena in the fields of acoustics and electromagnetics.