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A stable volume integral equation formulation and its discretization for extremely anisotropic materials is presented. The volume integral equations are written in terms of the volume equivalent currents. The equivalent currents are expanded with piecewise constant basis functions, and the Galerkin's scheme is applied for testing the equations. Numerical results show that the behavior of the formulation is more stable than the behaviors of the more conventional volume integral equation formulations based on fluxes or fields, when the scatterer is extremely anisotropic. Finally, the developed method is applied to analyze a highly anisotropic material interface which approximates the ideal DB boundary.