In this paper, theoretical analysis of longitudinal free vibration was carried out for Tb-Dy-Fe series magnetostrictive actuator and transducer. The formulations considered two constitutive laws; in one we employ the standard square nonlinear constitutive equation of magnetostriction and in the other we employ the linear piezomagnetic equation. The results obtained from the nonlinear equation can be reduced to the linear piezomagnetic equation when the amplitude of the excitation magnetic field provided by the coil is very small compared to the bias magnetic field and its frequency does not induce resonance of the system. For the case of a relatively large excitation magnetic field, which usually exists for an actuator, the nonlinear constitutive equation should be adopted in order to provide an accurate prediction for the design and analysis of actuator and transducer. Another important aspect is the resonance of the Tb-Dy-Fe series transducers that was revealed in the analysis using the nonlinear constitutive equation. The resonance not only appears at the natural frequencies of the system, but also arises when the frequency of excitation current in the coil happens to be half of one of the natural frequencies of the system. This conclusion cannot be reached using the linear piezomagnetic formulation.