Waves propagating on the surface of a three–dimensional ideal fluid of arbitrary depth bounded above by an elastic sheet that resists flexing are considered in the small amplitude modulational asymptotic limit. A Benney–Roskes–Davey–Stewartson model is derived, and we find that fully localized wavepacket solitary waves (or lumps) may bifurcate from the trivial state at the minimum of the phase speed of the problem for a range of depths. Results using a linear and two nonlinear elastic models are compared. The stability of these solitary wave solutions and the application of the BRDS equation to unsteady wave packets is also considered. The results presented may have applications to the dynamics of continuous ice sheets and their breakup.