Effect of rotation in a axis symmetric vibration of a finite, homogeneous transversely isotropic solid bar immersed in a fluid is studied using the linearized, threedimensional theory of elasticity. The equations of motion of solid and fluid are respectively formulated using the constitutive equations of a transversely isotropic solid bar and the constitutive equations of an inviscid fluid. Two displacement potentional functions are introduced to uncouple the equations of motion. The computed non-dimensional frequency, phase velocity and attenuation are presented in the form of dispersion curves for the material Zinc.