We have developed a forward-modeling method to compute the response of a triaxial induction logging tool in a layered biaxial anisotropic dipping formation without borehole and invasion zones. The purpose of this development is to provide a fast-forward computation algorithm to handle cracks in transverse isotropic (TI) formations in oil exploration, which is a mathematically challenging problem for log data inversion. We solve for the spectral-domain transverse electromagnetic (EM) field equations, propagation matrix, and reflection matrix in a biaxial anisotropic planarly layered media. The EM fields in the space domain are obtained by a 2D inverse Fourier transform. We derive formulations of the EM fields generated by three orthogonal transmitting coils in a fully anisotropic layered media. The proposed formulations are based on arbitrary relative dipping and azimuthal and tool angles; thus, we obtain the full coupling matrix connecting source excitations and magnetic fields anywhere along the tool axis. Computation results using this method in the response of triaxial induction tools in several cases were compared with published data in TI formations and biaxial layered formations. Our results agreed very well with the published data.