In this study, we used a computer simulation to investigate the effects of the coil current waveform and direction on the excitation processes of the nerve axon in inhomogeneous and anisotropic conducting media in magnetic stimulation. We assumed that the nerve axon was located in the media with 2 regions having different conductivities or electrical anisotropy that simulate different tissue types. The distribution of induced electric fields was calculated with the finite element method (FEM). The nerve fiber was modeled after equivalent electrical circuits having active nodes of Ranvier. The direction of the coil current at the intersection of a figure-eight coil was assumed to flow perpendicular to the nerve axon. We observed the excitation threshold when the coil current waveform and direction are changed with varying the electrical properties such as tissue electrical conductivity and anisotropy. The simulation results show that the threshold decreases with the increase of conductivity ratio between 2 regions and it also depends on the coil current waveform and direction. Biphasic coil current has lower threshold than monophasic one when the current direction is the same in both waveforms. The results also suggest that the tissue anisotropy strongly affects the excitation threshold. The threshold increases with the increase of tissue anisotropic ratio of longitudinal direction to the transverse one respect to the nerve axon. The results in this study give useful information to explain the experimental results of the magnetic stimulation of human peripheral nervous systems and the theoretical model is applicable to understand the characteristics in magnetic stimulation of both peripheral and central nervous systems.