One of the bottleneck in the finite element analysis is the mesh generation for the domain with complicated configuration. For this reason, many mesh generation algorithms has been developed in recent years. However, automatic mesh generation for three dimensional problem is still not reliable and sometimes not possible. The domain composition method is one of the analysis concept which reduces the cost of the mesh generation. By regarding the domain as a set of overlapping simple geometries, it is possible to solve the problem not with a global mesh but with meshes of simple geometries. In this paper, we formulate the domain composition method for two dimensional linear elastostatics and propose a new technique of stiffness elimination in order to get accurate results. In addition to the formulation, we show the availability of the method by implementing it into the commercial finite element program. Several results obtained by the proposed method are compared with those of conventional finite element analysis to represent the accuracy of the method.