Tidally-generated, trapped motions can significantly enhance and modify sea level and currents in the island proximity. The analytical solution for incident waves interacting with a cylindrical island with a circular sill has been constructed to investigate this phenomenon. To derive solutions for the scattering problems simple Sverdrup and Kelvin waves are used as incident waves. The amplification of the signal along the island perimeter has shown to be a function of frequency, relative dimensions of the island and the circular sill surrounding the island, relative sill depth, and the bottom friction. Although the incident diurnal tide may be amplified through the resonant response, this resonance occurs in the shallow water where the bottom friction damps the effect. The dispersion equation shows that the geometry of the problem favors amplification of semidiurnal tides. Analytical solutions obtained by superposition of the incident and scattered waves around an island are used to explain the observed peculiarities of tides in the vicinity of the Pribilof Islands, Bering Sea.