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In the present paper, we use a monolithic finite element method to simulate the flutter behavior of two, three and four parallel plates experimentally studied by Schouveiler and Eloy (Phys. Fluids 21, 081703(2009)). Different coupled fluttering modes of the parallel plates are successfully reproduced. Although the results are preliminary, the essential physics of this strongly coupled system are successfully captured. No artificial constraints (i.e., the virtual spring connections between the plates) are needed to predict the in-phase mode of flutter. To the authors' best knowledge, this is the first time that one can capture all the coupled modes of flutter of multiple plates through direct numerical simulations.