Abstract: The study focuses on the contact nonlinear computation method for multi-subassemblies interaction, and tries to verify the extendibility of the method proposed by Likhachev and the viability of resolving CEFR subassembly contact problem. Based on the computation method developed by Likhachev, the consistent deformation conditions and the system potential energy equations for multi-subassemblies are established at three contact levels instead of two levels. The minimum potential energy principle is utilized to acquire the contact forces. For simplicity, orthogonal transform and Lagrangian-double-problem transformation are used. Finally, the nonlinear contact analysis turns into the optimization of a quadratic function with conditional inequality constraints. Conclusions are as follows: Likhachev method can be extended for three contact levels from two, and is generally practicable; the final derived expression is a common problem in optimization theory, which could be easily solved numerically.