The linear stability problem for a number of models of the mantle of the earth is considered. For appropriate values of the physical parameters of the mantle it seems likely that the Rayleigh number for mantle‐wide convection is far in excess of the value necessary for marginal instability. For very high Rayleigh numbers the velocities in the models can be derived from solutions for turbulent convection. But even for very high Rayleigh numbers the inhomogeneity in Bullen's region C is amply strong enough to prevent mantle‐wide convection from occurring, whether the inhomogeneity involves a phase transition or represents a chemical inhomogeneity. Convection on a smaller scale is also considered. Convection in the upper mantle may occur. These events are not widespread and are of small scale, having dimensions of about 1200–1500 km in lateral extent and depths of the order of 400 km. Large Rayleigh numbers and associated turbulent convection are not ruled out for the lower mantle. The conclusions depend crucially on the assumptions of the values of the viscosity and of the strength of the mantle. The model of turbulent convection in the lower mantle is consistent with localizing a material of high strength and high viscosity in the upper mantle and with the observation that earthquakes are not observed to occur in the lower m