The EMT 140 is a plate reverb that exploits the vibrations of a metallic plate to simulate reverberation. It was an industry standard in the 60s and 70s, and its sound is still widely appreciated nowadays. In this work, a physical model of the EMT 140 is developed, by adopting a modal approach. First, a modal decomposition of the plate vibration is performed; then, a physically-based model for damping is presented, based on previous works, including a simulation of the controllable damper present on the real unit. The modes equations then are discretised with an exact numerical integrator. As physical models are quite computationally expensive, here an optimisation technique is also presented, based on linear least squares. Results show that the optimisation could reduce the computational time by 80%, while still maintaining a high sound quality.