It is well known that many conforming plate finite element spaces in the multilevel methods are nonnested even when the triangulations are nested, so it is difficult to construct the effective V-cycle multigrid method and multilevel preconditioners for the plate bending problem. In this paper, a new method dealing with multilevel methods for finite element discretisation equations of the plate problem is developed. An optimal V-cycle multigrid method and multilevel preconditioners for some famous conforming plate elements are constructed. Moreover, our methods can be applied to the plate problem with complicated geometries.