This study uses the strain energy approach to present a fundamental analytical expression for the moments and deflection of a circular elastic plate resting on a Winkler foundation. Parametric analysis is performed to assess the location of the plate liftoff and how the deflection profiles changed, with a view to contrasting the pattern of variation reported in the literature using an approximation solution method. It comes to light that the plate’s point’s radial distance of lift-off decreases more for lower values of the foundation soil’s subgrade coefficients. Furthermore, it has been found that variations in the soil’s subgrade conditions can cause a considerable fluctuation at any radial distance in the plate’s deflection, particularly at lower values of the modulus of subgrade reaction. The present formulation has exceptional performance, precision, and applicability.