In this paper, we calculated the strain distribution of low dimension structure using the elastic continuum model in the first part we focused on the lens-shaped quantum dot, and discussed the strain distribution of the quantum dot with and without capping layer. In another section, we gave a detail analysis about the strain distribution for quantum wire and quantum dot intergrowth structure, and there are two situations: the first, a little bigger quantum dot grown within a single quantum wire, the second, Y shaped quantum wires where quantum dot grown in the cross section of the wires, and the angle of the Y shaped wires lessen than 12 degree. All the low-dimension structures discussed have been observed in the laboratory. For the lens-shaped quantum dot with and without capping layer, the results showed that in both circumstances, the strain distribution would become more uniform in the quantum dot if the transverse size becomes larger. Compared with the open quantum dot (without capping layer), the capping layered quantum dot has a more sufficient strain relaxation, and even excessive strain relaxation is observed in the simulation. This phenomenon can be used to qualitative explain the quantum dot cave in and cavern out in the sequential capping layer growth interruption observed in laboratory. It is very promising for the quantum wire and quantum dot intergrowth structure. The phenomena of photoluminescence spectrum not changing with the variation of temperature have been observed recently in the intergrowth structure. For convenience, we used a simplified model to calculate such a structure, which we adopted rectangle quantum wire and rectangle quantum dot. The growth is along the  direction, and the wire is along the  direction. The results showed that the strain in quantum dot is greatly enhanced in the intergrowth structure compared with the single quantum dot system. There are strain-focusing region around the interface of quantum dot and quantum wire.