A theoretical model of tsunami generation and propagation near an oceanic island is developed in this paper. The solution is computed by means of a method that is basically analytical and that synthesizes waveforms as a superposition of normal modes whose evolution is governed by the linearized shallow‐water equations. Sea‐bottom deformations are computed analytically via the classic dislocation theory applicable to plane faults with uniform slip. Initial sea‐surface elevations are assumed to be equal to floor displacements. The ocean basin circling the islands is supposed to have a depth depending only upon the distance from the island center. Tsunami propagation is computed in the whole basin with particular attention to the wave invading the island coasts. It is seen that a typical open‐ocean radiation pattern combines with diffracted wavefronts and wavefronts progressing around the island that tend to persist for a longer time after the first tsunami attack. These local island waves are particularly interesting because they extend the tsunami menace even to the coastline segments potentially protected from the main tsunami attack.