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The effect of ferromagnetic shields on the self and mutual inductances of the wires enclosed by a ferromagnetic shell has been theoretically analyzed. Some theoretical equations based on a simplified model, which assumes that the driving wires and returning wires are located within two separated magnetic shells, are derived. The analysis shows that the effect of the ferromagnetic shells on the inductance of the wires depends strongly on the separation of the two magnetic shells; the closer the two magnetic shells, the stronger the effect. For a configuration of two identical ferromagnetic shells of internal radius 0.65 cm and separated by 10 cm, it is estimated that the self and mutual inductances are increased by about 30 percent for a wire of radius 0.06 cm. The changes of the self and mutual inductances are essentially due to the interactions between the ferromagnetic shells and the induced fields of the current elements.