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Accurate electromagnetic (EM) analysis for conductive media requires to consider the finite conductivity of the media. Although the problems can be formulated by surface integral equations (SIEs) with an approximate surface impedance, we treat the conductive media as penetrable objects and use volume integral equations (VIEs) to exactly describe their EM features. The VIEs are solved by a point-matching scheme which does not rely on any basis and testing functions and allows the use of nonconforming meshes. Since the VIEs are well-conditioned in general and the integral kernels are free of material parameters, the scheme is flexible to accommodate a wide range of skin depth. Moreover, when the skin depth is small, we can only discretize the skin domain with a current distribution to reduce the cost. For large conductive media, we also incorporate the scheme with the multilevel fast multipole algorithm (MLFMA) to accelerate the solution. Typical numerical examples are presented to illustrate the scheme and its effectiveness has been validated. [ABSTRACT FROM PUBLISHER]