Using the multipoles method, we formulate the problems of diffraction (both surge and heave) of water waves by a submerged prolate spheroidal body in deep water with an ice-cover, with the ice-cover being modelled as an elastic plate of very small thickness. It investigates the linear hydrodynamic diffraction problem by prolate spheroidal body and obtained the analytical solution for the associated boundary value problem. The structural model is a spheroidal with its polar axis greater than its equatorial diameter, subjected to the action of incident wave. The hydrodynamic forces (Surge and heave exciting forces) are obtained and depicted graphically against the wave number for various parameters and also the flexural rigidity of the ice-cover to show the effect of the presence of ice-cover on these quantities. When the flexural rigidity is taken to be zero, the numerical results for the forces for water with free surface are recovered.