This research presents a study on numerical techniques to model the electromagnetic propagation in geophysical formations commonly encountered in oil well drilling. The employment of electromagnetic sensors surrounding the drill bit allows inferring the constitutive parameters of the soil around the well. In recent years, advances in electromagnetic logging technology have enabled the real-time modeling of this problem. In this way, the drilling direction can be guided in order to maximize the exploitation of oil, gas, and other fossil hydrocarbons. The complex geophysical formations that are prevalent in this type of problem can be effectively handled using brute-force numerical techniques such as finite-differences, finite-elements and finite-volumes. However, these techniques suffer from relatively high cost in terms of both computer memory and CPU time. The advancement of real-time logging technology demands approaches that are more efficient than purely numerical methods. In this work, we employ the mode-matching technique combining attractive features of the well-known pseudo-analytical approaches to obtain a new technique for analyzing directional well-logging tools in anisotropic formations with both radial and axial stratifications. The proposed technique allows to model problems not yet explored, but with a strong technological motivation, such as electromagnetic propagation along curved wells and drilling along inclined layers. We present a series of validation results showing that the novel technique introduced in this study can model accurately and efficiently electromagnetic logging sensors used in oil and gas exploration.