The formation of discontinuities within internal gravity waves in a rotating Boussinesq atmosphere is investigated with a numerical model. The motion is bounded between two rigid horizontal boundaries, and heating and friction are neglected. Special sinusoidal initial conditions are used. The equations are integrated for a range of values of the initial Rossby (Ro) and Froude (Fr) numbers. Discontinuities are found when the following conditions are satisfied: Fr?0.2 and Ro?0.2. These results are substantially different from those obtained for a one-layer fluid with a free upper surface.