The variable geometry trusses (VGTs) can purposefully vary their geometric configuration as well as their physical properties. The VGTs consist of repetition of a truss unit in which some of the truss members can vary their lengths continuously using actuators. In this paper, it is considered to obtain the global optimum geometry of twodimensional VGT of multiple units for maximizing structural stiffness against the external static load. Multi-degree of freedom of the VGT makes it difficult to obtain the global optimum geometry out of many local optima using the traditional gradient-based algorithms. To overcome this difficulty, we have proposed a tnneling method, which is one of the approaches for global optimization. From the result of numerical examples, the efficiency and reliability of the proposed method are discussed in comparison with the parametric results.