The normal mode instability problem for a stationary Rossby wave of finite amplitude and arbitrary orientation in a two-level model with zonal mean shear in the vertical is examined on the infinite beta-plane using a Floquet technique. The results are compared to the instability of a finite amplitude stationary Rossby wave in a barotropic model. The instability of the barotropic model linearized about the upper level flow of the stationary two-level Rossby wave is also examined; forcing must be introduced to the barotropic equations in this case to balance the time tendency of the basic state.