Under the action of external loads, the critical condition of fracture in ductile materials is closely re-lated to the strong interactions among internal microdefects at the later stage of deformation. By means of Riemann's analytical integration, necessary conditions for the internal necking between adjacent elliptical voids under plane strain conditions are studied. The influences of the aspect ratio of elliptical voids, the distance between two voids, and the angle of the straight line connecting the central points of two voids with respect to the tensile direction on the above-mentioned necessary conditions are also discussed.