Abstract: Discussing the giant magnetostrictive material in the longitudinal exciting magnetic field and introducing the Maxwell's equation to obtain the magnetic field distribution function in terms of Bessel function within the giant magnetostrictive material, the Kelvin expression of magnetic field in giant magnetostrictive material is given by the analytical method from Bessel function. A qualitative analysis is made to the magnetic field distribution to reveal the classical hysteresis characteristic of internal magnetic field. Based on the theory of magnetic energy, the eddy current loss within material is preliminarily discussed to get the expression of eddy current loss within material in terms of Kelvin function. Then, the effect of the influencing factors on eddy current loss are also discussed, such as exciting frequency, electrical conductivity and radius of giant magnetostrictive material, thus laying down a foundation on which the selection of proper parameters for giant magnetostrictive material parameters is available.