This paper deals with the numerical approximation of the bending of a plate modeled by Reissner-Mindlin equations. It is well known that, in order to avoid locking, some kind of reduced integration or mixed interpolation has to be used when solving these equations by finite element methods. In particular, one of the most widely used procedures is based on the family of elements called MITC (mixed interpolation of tensorial components). We consider two lowest-order methods of this family on quadrilateral meshes. Under mild assumptions we obtain optimal H1and L2error estimates for both methods. These estimates are valid with constants independent of the plate thickness. We also obtain error estimates for the approximation of the plate vibration problem. Finally, we report some numerical experiments showing the very good behavior of the methods, even in some cases not covered by our theory.