A numerical method based on spectral expansions is given for the computation of vorticity waves arising from shear instability of a longshore current. This method allows for any mean flow profile and any beach topography (remaining constant alongshore and with a straight shoreline). The shallow-water equations are considered without any assumption about the sea surface (such as rigid lid), and dissipative terms accounting for bottom friction and/or eddy viscosity are included. A numerical simulation for some flow profiles that are quite realistic in the surf zone and for several bathymetries is presented. For inviscid flow the predictions of the Bowen and Holman (1989) analytical model for a very simplified geometry are found to give rise to the main features. However, the details in the flow and depth profiles are found to significantly influence the instability curves, especially for a barred beach. For the fastest growing mode, the wavelength is between 1.7 and 2.7 times the width of the mean current l. Frequencies of about 0.09fs, where fs is the maximum shear at the sea face of the current profile, and an e-folding time of the exponential growth that is roughly equal to the wave period are obtained. The phase speed is between 0.5 and 0.7 of the mean current peak. Dissipation has a considerable effect on the wavenumber span and the growth rate of the instability, so reasonably constant values of the eddy viscosity and realistic values of the Chezy coefficient can entirely remove the instability. The phase speed of neutral shear waves is analytically found to be equal to the mean flow velocity at the cross-shore location where the potential vorticity has an extremum. This velocity is found to give an estimate of the phase speed of growing modes. We found that the rigid-lid assumption tends to overestimate the growth rates by an amount which depends on the maximum Froude number of the mean flow. The instability curves and the dispersion lines for a free surface converge towards the rigid-lid ones when the Froude number decreases, and the rigid-lid assumption is therefore valid for a low Froude number. ¿ American Geophysical Union 1994