  In this paper, we study the mixed element schemes of the Reissner-Mindlin
plate model and the Kirchhoff plate model in multiply-connected domains. By a
regular decomposition of $H_0({\rm rot},\Omega)$ and a Helmholtz decomposition
of its dual, we develop mixed formulations of the models which are equivalent
to the primal ones respectively and which are uniformly stable. A framework of
designing uniformly stable finite element schemes is presented, and a specific
example is given.
