The integral equation method is used for induced-polarization (IP) and electromagnetic (EM) modeling of a finite inhomogeneity in a two-layer anisotropic earth. An integral equation relates the exciting electric field and the scattering currents in the homogeneity through the electric tensor Green's function deduced from the vector potentials in the lower layer of the earth. Digital linear filtering and three-point parabolic Lagrangian interpolation with two variables speed up the numerical evaluation of the Hankel transforms in the tensor Green's function.The results of this integral equation method for isotropic media are checked by direct comparisons with results by other workers. The results for anisotropic media are indirectly verified, mainly by checking the tensor Green's function. The calculated results show that the effects of anisotropy on apparent resistivity and percent frequency effect are to reduce the size of the anomalies, shift the anomaly region downward toward the lower centers of the pseudosections, and enhance the effect of overburden; in other words, to shade the target from detection. This is due to the increase of currents flowing horizontally through the earth over the target. The effects of anisotropy on horizontal-loop EM responses are to reduce the amplitude and lower the critical frequency of the maximum of the quadrature component.