Abstract: In the study of elastodynamic problems of inhomogeneities, a kind of integrals of the type Φ=∫∫_Ω∫ρ(X') exe(iαR)/Rdv' are frequently presented. In this paper the problems caused in evaluating Φ-integrals by Taylor series 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 important part not only in the elastodynamics problems of inhomogeneities but also in the integration of inhomegeneous Helmholtz equation associated with the problems of wave phenomena in the fields of acoustics and electromagnetics.