An engineering investigation into the dynamics and vibrations of magnetostrictive transducers is conducted. The transducers are examined from a linear systems perspective. The system input is electric current. The system output is displacement. A comparison is made between the classic low-signal linear transduction equations for the material and those for the electromechanical transducer containing the material. A magnetomechanical model is derived assuming the magnetostrictive rod behaves as a linear spring. The model is an expression for the complex valued, frequency, coupling, and load dependant magnetic permeability of the magnetostrictive material within the transducer. One-dimensional analytical constant parameter linear electromagnetic models of cylindrical magnetostrictive transducers are derived for the steady state, oscillating magnetic field strength as a function of radial position, electric current, and excitation frequency, H(r,l,[omega]). The first electromagnetic model is the classic solution for a cylindrical conducting rod in a wound wire solenoid. The second electromagnetic model is for cylindrical transducers with an external conducting cylindrical housing. Both models neglect end effects. The results are electromagnetic-magnetomechanical models of cylindrical magnetostrictive transducers including both the effects of eddy currents occurring within the transducer's components and dynamic effects. The models are formulated to calculate electrical impedance functions, Z[subscript]ee([omega]), as would be measured at the electric terminals of the transducers when run in their linear range of operation with a known load. Both models simulate the distinctive characteristics of a coupled electromechanical system, i.e., large variations with frequency occur in the electrical impedance magnitude and phase near the mechanical resonant frequency. Numerically disabling dynamic effects allows the calculation of what would be the blocked electrical impedance of the transducers, Z[subscript]e([omega]). Knowledge of Z[subscript] ee([omega]) and Z[subscript] e([omega]) allows calculation of the transduction coefficients, including the effects of eddy currents and the mechanical load connected to the transducer. From there, quantities of engineering interest can be calculated. Comparisons are made between experimental measurements and model simulations of transducer electrical impedance functions, and transducer displacement from current frequency response functions. Simulations of impedance and displacement were typically ±10% of experiment.