  A nonlinear Schr\"odinger equation for the envelope of two dimensional
surface water waves on finite depth with non zero constant vorticity is
derived, and the influence of this constant vorticity on the well known
stability properties of weakly nonlinear wave packets is studied. It is
demonstrated that vorticity modifies significantly the modulational instability
properties of weakly nonlinear plane waves, namely the growth rate and
bandwidth. At third order we have shown the importance of the coupling between
the mean flow induced by the modulation and the vorticity. Furthermore, it is
shown that these plane wave solutions may be linearly stable to modulational
instability for an opposite shear current independently of the dimensionless
parameter kh, where k and h are the carrier wavenumber and depth respectively.
