An attempt is made to explain the growth process of creep cavities wherein the diffusion mechanism is not applicable. When a screw dislocation reaches grain boundary, the dislocation starts to move on the different slip plane by cross-slip. But such movement of the dislocation is interrupted at a precipitated particle located near the grain boundary, and the dislocation moves back to the grain boundary by another cross-slip. Thus the dislocation moves along the grain boundary with successive cross-slip, until it is absorbed by a cavity in the boundary, resulting in growth of the cavity. The rate of the growth of cavity is calculated and the relationship between creep rupture time and creep rate is determined.The effect of coarsening of precipitate particles upon the creep rupture time is discussed. In the case of no particle coarsening dung creep, the creep rupture time tr is inversely proportional to the minimum creep rate em. However, tr is proportional to em-0.6 when the coarsening of particles takes place during creep. The theory is well consistent with the experimental data obtained for type 316 and 347 stainless steels.