The ELCUT program was used to model the penetration of the magnetic field of a dipole magnetized along a ferromagnetic tube’s axis through the tube wall. It was found for the first time that the induction of the dipole’s magnetic field increases after penetration though the ferromagnetic tube as compared to the field without this tube. It has been found that, near the dipole central cross section normal to the tube’s axis, the field is weakened (screened) by the tube, whereas, far from the dipole center, the field along the tube’s axis increases several times. It has been shown that the tube-induced field-screening and field-amplification coefficients are functions of the distance between the observation point and the dipole center, which is a field source.