We develop the analytic solutions to a two-dimensional, shallow-water model of the high-latitude thermosphere. The equations are a linearized representation of the response of the neutral atmosphere to the momentum source due to the plasma convection pattern. Our results show how the neutral winds depend on the Pedersen and Hall ion drag coefficients and the horizontal wave number. The response depends on the dimensionless sale as it appears in the product of the Rossby radius of deformation and the wave number. The flow pattern is shifted in local time from the plasma flow pattern by an amount that depends on the average electron density. At the largest scales there is a 180¿ phase shift between the rotational flow components in the E and F regions. The model applies to quiet magnetic conditions and below 200 km of altitude.