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The shallow water, linear model in cylindrical coordinates is used to investigate barotropic and inertial instabilities in the tropical cyclone outflow layer. When the mean state wind satisfies the condition |ζ|«|f 0 the instabilities found in our model are equivalent to the barotropic instabilities calculated with the quasi-geostrophic potential vorticity equation. The maximum instability is internal and appears at azimuthal wavenumber one. When an observed (composite) hurricane outflow layer is assumed as a basic state, the largest barotropic growth rate (e-folding time scale ≈7 days) appears at azimuthal wavenumber s = 1 and equivalent depth about 30 m. The maximum growth for s = 2 is about four times smaller than for s = 1 and occurs with the external mode. Inertial instability dominates at the very small equivalent depths and is likely to be stabilized by friction.