In the long-period oscillations of sunspots the time-variations of magnetic field and the variations of their umbral brightness change in the anti-phase regime: when the spot as a whole shifts up, its magnetic flux tube expands, the magnetic field decreases, and the brightness of the umbra increases slightly; and vice versa, when the magnetic tube of a spot goes down, its field increases slowly and the umbral brightness decreases. This process is fully consistent with the Bierman's idea and the theoretical model of shallow sunspot.