The nonlinear equations of an elastic tank-liquid coupling system subjected to the external excitation are established. By means of the multi-scale method and the singularity theory, the bifurcation behaviors of the system are investigated and analyzed. The various nonlinear dynamical behaviors of the coupling system are obtained, which can further explain the relationship between the physical parameters and the bifurcation solutions. The results provide a theoretical basis to the realization of the parameter optimal control.