A persistent and large scale galactic spiral structure might be the result of resonant excitation of density waves, forced in the low viscosity interstellar gas, by the gravitational field of an asymmetric stellar structure (galactic nucleus, condensation, companion galaxy, etc.) rotating like a rigid body around the galactic centre. This paper deals with this problem in the simple case of a homogeneous plane viscous medium of infinite extent, in a state of rigid body rotation. Numerical estimates are given in the case of density waves excited by the gravitational field of a central dumb-bell. They show that the mechanism of hydrodynamic gravitational resonance is worthy of a further, more realistic, treatment.