The scattering analysis with the Electric-Field Integral Equation by the Method of Moments of perfectly conducting plates is normally carried out through the thin-plate approximation, which models the closed surface as an open surface and discards the influence of the plate rim. The resulting accuracy is accepted in many practical applications as long as the thickness of the plate is small enough. However, in the scattering analysis of plates with grazing incidences, the thin-plate approximation gives rise to severe inaccuracies. In this paper, we present a new numerical approach, which we name thick-plate formulation, for the accurate computation of the current and the RCS for a plate with nonzero thickness. Our scheme provides similar accuracy as the solution obtained with the full modelling of the plate and with less computational time.