The motion of point defects is random. In the present paper the influence of the stochastic fluctuations of the point defect concentrations in the close vicinity of a void on the void ensemble kinetics is investigated. The investigation is based on the kinetic equation for the void distribution function in the size space. The analysis of the spatially homogeneous void distribution function behavior in the size space gives the condition for which this function has no maximum around the average void size and decreases monotonously in the whole interval of void sizes. The disappearance of the void distribution maximum around the average void size corresponds to the instability of the ensemble of randomly distributed voids induced by the stochastic fluctuations and to the shrinkage of some number of voids. In the presence of the instability the qualitative behavior of the spatially inhomogeneous void distribution function is also discussed. It is shown that the instability considered can lead to the formation of spatially ordered void structure.