This paper presents a novel technique for the computation of eigenvalues and eigenvectors of partially\ud enclosed basins such as harbours and bays. The procedure makes use of the finite element approximation\ud of the linear shallow water equations, and converts the time-depending problem into an eigenvalues one.\ud The main point of novelty of this research is the mathematical condition used at the boundary that separates\ud the computational domain from the open sea. While classical techniques impose a zero surface elevation (i.e.\ud a nodal line), here an approximate radiation condition is applied. The use of a radiation condition at the open\ud boundary gives a quadratic eigenvalue problem that admits as solution complex eigenvalues and eigenvectors,\ud thus describing the flow in terms of both standing and progressive waves. The new method is applied\ud to an idealized long and narrow harbour, for which an analytical solution of long wave resonance exists,\ud and to the harbour of Marina di Carrara (Italy), for which measurements and previous numerical computation\ud results are available. In both cases the results show good agreement with the available data