We consider a two-dimensional incompressible inviscid fluid with variable density, under the action of gravity. We assume that the equilibrium density profile is stable, and we consider the so-called Boussinesq approximation, which neglects density variations in terms which do not involve gravity; this system has been widely used in physical literature to describe internal gravity waves. We prove a modulational instability result for such system, namely that the linearization at a small-amplitude travelling wave admits at least an eigenvalue with positive real part. This can be regarded as a rigorous proof of the phenomenon of Parametric Subharmonic Instability (PSI) for inviscid fluids, in which one observes a transfer of energy between a primary initially excited wave and two secondary waves with different frequencies. This is a joint work with R. Bianchini (CNR) and A. Maspero (SISSA).