The stability of a recently proposed general relativistic model of galaxies is studied in some detail. This model is a general relativistic version of the well-known Miyamoto-Nagai model that represents well a thick galactic disc. The stability of the disc is investigated under a general first-order perturbation keeping the space-time metric frozen (no gravitational radiation is taken into account). We find that the stability is associated with the thickness of the disc. We find that flat galaxies have more non-stable modes than the thick ones, i.e. flat galaxies have a tendency to form more complex structures like rings, bars and spiral arms.381414991507