<p>This paper focuses on explaining the presence of ice cover in the linear surface wave scattering and radiation by a circular cylinder submerged in a finite-depth ocean. The ice cover has the property that it behaves like a thin elastic plate. Under small-breadth structural oscillations, analytical expressions of the three-dimensional problem are derived in each flow region for the wave motion by an eigenfunction expansion method. However, the velocity potentials of the incident and scattered waves involve the Bessel and Hankel functions for each region. To get complete analytical solutions, we solve the obtained integral equations by the multi-term Galerkin method, where the ultra-spherical Gegenbauer polynomial is chosen as a basis function. This logical approach gives rapid convergence and provides six-figure delicacy in the results of hydrodynamic quantities. The hydrodynamic quantities acting on the rigid cylinder are shown graphically against the frequency. The study also highlights the significance of crucial parameters such as depth, radius of the cylinder, and flexural rigidity of the ice cover to design the breakwater. Based on the numerical results, it can be concluded that the present cylindrical breakwater design is quite capable of attenuating the wave forces and roll moment amplitudes.</p>