Bifurcation problems both for static and dynamical cavitation in a solid sphere composed of the incompressible hyperelasticplastic material, under uniformly distributed tensile boundary dead load were studied. For each problem, cavity forms at the center of the sphere when the tensile load is larger than its critical value. Bifurcation curves and the growth curves for the plastic deformation region were given. For static cavitation, the deformation displays three stages, namely, fully elastic, elasto-plastic and fully plastic stages. For dynamical cavitation, the cavity grows without bound and the sphere displays plastic flow.
