We consider an analytical model of the 1/f noise in semiconductors linking this noise to the tail states in the energy gap near the edges of the conduction or valence band. We also report on the numerical calculations confirming the analytical model. The noise has the 1/f spectrum only if the capture cross-section of the tail states changes with energy with the characteristics energy, which is smaller than the thermal energy. The noise level should have a maximum when the Fermi level lies in the vicinity of the bottom of the conduction band or of the ceiling of the valence band (several thermal energies away either in the energy gap or in the conduction or valence band). Our results also show that the noise is fairly insensitive to the exact energy dependence of the density of the tail states.