The stability of the classical Norwegian polar front model is investigated, using a numerical technique to supplement the more precise conclusions which are possible in the limiting cases of zero density difference or zero wavenumber. The feasibility of the numerical technique depends on a careful formulation of boundary conditions at the limits of the frontal zone. The numerical results cover the region of Rossby number (Ro) ≤ 3 and Richardson number(Ri) ≤ 5, but their interpretation is unclear at Ri > 2 and Ro > 1. Unstable waves exist at all wavelengths; Rayleigh shear instability at small Ri, Helmholtz shear instability at large Ro and small Ri, shear instability and geostrophic baroclinic instability simultaneously at small Ro and Ri > 2, and a combination of geostrophic and Helmholtz instability when Ri > 2 and Ro < l (but not too small). The previous conclusion of Kotschin that this frontal model is stable for Ri < 2 is therefore incorrect.