This paper reports an analytical and numerical study of natural convection in a shallow enclosure filled with a non-Newtonian fluid. Thermal boundary conditions of the Neumann type are applied on the horizontal walls of the enclosure while the vertical walls are assumed adiabatic. A power law model is used to characterize the non-Newtonian fluid behavior of the fluid. The governing parameters for the problem are the thermal Rayleigh number Re, power-law index n, Prandtl number Pr and cavity aspect ratio A. An analytical solution, valid for an infinite layer, is derived on the basis of the parallel flow approximation. Rigid-rigid, free-free and rigid-free hydrodynamic boundary conditions are considered. It is demonstrated that, for shear-thinning fluids, the onset of convection is subcritical. For shear thickening fluids, convection is found to occur at a supercritical Rayleigh number equal to zero. The effects of the non-Newtonian behavior on the fluid flow, temperature field and heat transfer are discussed, A good agreement is found between the analytical predictions and the numerical results obtained by solving the full governing equations. (C) 2013 Elsevier B.V. All rights reserved.