In this paper, the electrical properties of the Fe/MgO/Fe tunnel system are studied using an original technique, in which upper metal element was an iron probe inserted into the dielectric in a controlled manner. This makes it possible to study the electrical properties of the Fe/MgO/Fe system upon changing the physical parameters such as contact area and dielectric thickness. Based on the obtained results of the conductivity measurements, the corresponding approximation coefficients are determined. This allows to analytically calculating the $I–V$ characteristics in a wide range of dielectric thickness and contacting area. It is established that the resistance of the Fe/MgO/Fe system is non-monotonically dependent on the dielectric thickness and growth in $\sim$ 3 times when the MgO thickness increases by 0.21 nm. An increase of the contact area leads to a linear decrease of the resistance of the Fe/MgO/Fe system while preserving the value of current density and approaching the experimental $I–V$ characteristic to a linear dependence. This effect is attributed to the influence of local areas of conductivity, arising due to the defects and impurities, on the specifics of the conductivity of the whole system. The thickness of the dielectric and the limit voltage, at which the tunnel type of conductivity is preserved, are determined from $I–V$ characteristics during the process of electrical breakdown of the dielectric. It was established that the dielectric strength increases to 6.6 MV/cm for the MgO thicknesses ranging from 1 nm to 4 nm and decreases to 6.2 MV/cm in the range from 4 nm to 10 nm.