With using new field and theoretical data, it has been shown that applying the electromagnetic field of transverse magnetic (TM) polarization will give new opportunities for electrical prospecting by the method of transient processes. Only applying a pure field of the TM polarization permits poor three-dimensional objects (required metalliferous deposits) to be revealed in a host horizontally-layered medium. This position has good theoretical grounds. There is given the description of the transient electromagnetic method, that uses only the TM polarization field. The pure TM mode is excited by a special source, which is termed as a circular electric dipole (CED). The results of three-dimensional simulation (by the method of finite elements) are discussed for three real geological situations for which applying electromagnetic fields of transverse electric (TE) and transverse magnetic (TM) polarizations are compared. It has been shown that applying the TE mode gives no positive results, while applying the TM polarization field permits the problem to be tackled. Finally, the results of field works are offered, which showed inefficiency of application of the classical TEM method, whereas in contrast, applying the field of TM polarization makes it easy to identify the target.