In the present paper, it is shown how one can employ existing rigid body codes to handle systems containing elastic plates by using a Rayleigh–Ritz discretization procedure. The equations of motion are formulated for a rectangular plate undergoing large rigid body motions but small elastic deformations. Geometric nonlinearities in the elastic coordinates are taken into account to include the effect of dynamic stiffening. As an example, a spin-up maneuver for a simply-supported plate is treated.