This paper explored the blade-bending, disk-transverse and shaft-torsion coupling vibrations phenomenon of a multi flexible disc rotor system, whose blades subsystem was grouped with spring. Being different from the author's previous researches, here we used two methods: one is the assumed mode method (AMM) and the other is the finite element method (FEM), the proposed former one is main, and the latter one is complementary. Then compared the two results generated from them. According to the authors' previous definition, a flexible disc rotor system displays three coupling vibrations' types, inter-blade (BB), shaft-disk-blade (SDB) and disk-blade (DB) modes. In this paper, the authors additionally defined two new types, which were called lacing wires-blade (LB) and lacing wires-disk-blade (LDB) mode. The system change rules of natural frequencies and that of mode shapes would be discussed. Some interesting results are shown in this paper. Firstly, the author pointed out the change rules of the mode shapes and natural frequencies by using the AMM and FEM (including three kinds of softwares). Secondly, numerical calculation results also showed that the distance of disk, the disk with flexible, the constant of spring, and location of spring four phenomena would affect the natural frequencies.