The Multiscale Finite Element Method (MsFEM) is a Finite Element type approximation method for multiscale problems, where the basis functions used to generate the approximation space are precomputed as solutions to problems posed on the elements of a coarse mesh and ressembling the global problem of interest. These basis functions are thus specifically adapted to the problem at hand. Once these local basis functions have been computed, a standard Galerkin approximation of the global problem is performed. The resulting method has a limited number of degrees of freedom (typically the same number as a standard method on the given coarse mesh), each of them being associated to a oscillatory basis function which encodes fine-scale details of the microstructure. In this talk, we show how to extend the method to the case of composite plates. These are materials occupying a three-dimensional domain which is very thin in the third direction. In addition, the mechanical parameters of the plate are assumed to be heterogeneous, with coefficients that rapidly vary in the in-plane directions. We consider several variants to build the basis functions and provide illustrating numerical comparisons, in particular for perforated plates.