Abstract: The stability of rigid rotor on support of anisootropical rigidity with a cavity chamber partially filled with fluid was studied on the basis of a two-dimensional inviscid rotating fluid model.The effects of the system parameters,such as fluid fill ratio,mass ratio,external damping and support anisotropical rigidity ratio,on the instability of the rotor system were considered.It is shown that there probably exist two unstable regions of the rotational speeds that correspond to the two critical speeds of the rigid rotor system.However,the anisotropical rigidity of the support does not always result in occurring two unstable regions of rotational speeds.The possibility of their occurrence also depends on other system parameters.Since the anisotropical rigidity of support always makes the unstable region of rotational speeds increase,it is suggested that the support of anisotropical rigidity should be avoided as possible.