This paper first points out that the mechanism of anti-resonances explained in many publications is not reasonable. Then, it presents the theoretical analysis on the anti-resonances of forced harmonic response for a system of two degrees of freedom, revealing the mechanism difference between the driving-point anti-resonance and the transfer anti-resonance, and the relationship between the anti-resonance and the node of a natural modeshape. Moreover, the paper demonstrates the above stated mechanism and relationship through a case study on the harmonically forced vibration of a rigid beam supported by two identical springs.