In this article, free and forced vibration behaviors of hollow spheres under dynamic internal pressure are investigated. The material is assumed to be transversally isotropic with respect to the radial direction. Solutions are obtained in the Laplace domain and transformation into the time domain is performed exactly by the theory of residues. Frequency equations for free vibration are derived explicitly. Closed-form expressions for radial displacement and hoop stress due to various dynamic internal pressures are presented allowing for parametric studies. An anisotropy parameter involving circumferential and radial stiffness is defined and the effect of anisotropy is parametrically investigated. To validate the results material properties available in the literature are used.