The stresses generated by breaking gravity waves in the mesosphere are calculated with a numerical model of steady vertically propagating gravity waves that includes wavelength dependent radiative dissipation and turbulent viscosity and conduction. The principal findings are (1) waves do not break for ‖u¿-c‖ values ≲20 m s-1 as radiative damping prevents wave amplitude growth with altitude for short vertical wavelengths; (2) the downward heat flux due to turbulence of breaking waves and turbulent heating through loss of wave energy could severely affect the global radiative energy balance; and (3) predicted zonal deceleration for steady breaking waves is stronger than required by Apruzese et al (1982) for the mean circulation. Gravity wave breaking may be an intermittent process; otherwise, gravity wave stresses would produce an adiabatic mesosphere with a zonal mean velocity close to the phase speed of the breaking wave. Diffusive transport of constituents and potential temperature by breaking gravity wave turbulence is shown to be important. In the cases of nitric oxide and atomic oxygen the vertical eddy diffusion coefficients are shown to be sensitive functions of their respective chemical loss rates in the mesosphere and lower thermosphere.