A kinetic model of stress-induced vacancy diffusion in pentagonal whiskers and rods is suggested to investigate the void evolution there. In the framework of the model, the Gibbs-Thompson boundary conditions are employed to identify the free surface effect on the vacancy flux while the elastic fields of the wedge disclination are involved to reveal the contribution of the bulk effect. It is shown that the void evolution mode in the hollow pentagonal whiskers and rods is strongly determined by the initial internal and external radii as well as the materials parameters describing the response of both the residual stress and the surface tension. The void evolution diagram and kinetic curves are demonstrated to elucidate the critical and optimal parameters of this phenomenon.