Abstract: The rigid-flexible coupling dynamics and frequency veering of a thin flexible plate on a rotating rigid body are further studied. The high-order coupling (HOC) dynamic model is derived by Lagrange's equations. The in-plane longitudinal shortening terms caused by lateral deformation, generally called non-linear coupling deformation terms, are considered here. Furthermore, all derived items associated with the non-linear coupling terms are retained completely in the HOC model. The HOC model can not only be applied in the small deformation case, but also in the large deformation case, and makes up the deficiency of the first-order approximation coupling (FOAC) model in the large deformation case. In addition, the frequency veering phenomena along with the corresponding mode shape variations are exhibited and discussed in detail. When two frequency loci veer, the nodal line patterns of the mode shapes switch their shapes each other, and the changes of the nodal line patterns are continuous in the mild veering region, while those in the abrupt veering region are discontinuous. The transitive frequency veerings among the multiple modes accompanied by mode shape transfer are also exhibited.