The model of a damped orthotropic rectangular plate resting on a Winkler foundation with a simple support has the fourth order differential equation governing it, which is reduced to a second order coupled differential equation by separating the variables. The coupled differential equation was solved using numerical schemes .The classical condition used as an illustrative example is the simple support condition. It is observed that damping plays a very significant role in the vibration of solid structures, as it has been shown that the deflection profile depends greatly on the damping ratio. The deflection profile also proves to be more stable in the presence of foundation coupled with viscous damping. The results obtained were discussed and graphically presented.