A numerical model for the propagation of tsunamis generated by earthquakes is applied to study the impact of the water waves against the coast of a circular island. The hydraulic source is modeled by means of the static deformation of the seafloor produced by an offshore seismic fault. The initial sea-surface disturbance is assumed to equal the seabed displacement that is computed analytically through the classical dislocation theory of plane faults with uniform slip. The wave propagation is described by means of the shallow-water approximation of the Navier-Stokes equations and is computed in a radially symmetric domain for which a quasi-analytical solution is available. The governing equations are solved numerically by means of a finite-element (FE) method making use of the Galerkin procedure, the mesh consisting of triangular elements of variable size. After a preliminary test of the numerical model against the analytical results, several simulations are performed by varying the fault location, dimension, and dip as well as by varying the radial profiles of the basin bathymetry. Most attention is devoted to studying the amplification of tsunami waves impacting the island coast. What is seen is that, depending on the source characteristics (namely, fault length, dip, strike, and distance from the island) and on the basin bathymetry, high amplifications (in the range 1 to 5) are normally obtained not only in the front of the island as is expected but also on the lee side of the island, because of positive interference of waves traveling around the island in both directions. Under particular conditions (downwardly concave bathymetry), the largest amplifications are found neither on the front side nor on the lee side, but at intermediate places along the island coast.