The thermal, kinematic, and dynamic structures of mantle plumes are modelled by a two-dimensional, natural convection boundary layer rising in a fluid with a temperature-dependent, power law constitutive relationship between shear stress and strain rate. An analytic similarity solution is found for the case of upwelling adjacent to vertical, isothermal, stress-free plane. Temperature, vertical velocity, shear stress, and effective viscosity profiles are calculated for upwelling from a depth of 400 km in a mantle with either a Newtonian or a non-Newtonian olivine rheology and for plume ambient mantle temperature differences between 100¿C and 400¿C. The temperature excess of dry olivine plumes is limited by the constraint of subsolidus conditions. If inhomogeneities with concentrated heat sources exist in the mantle, thin thermal boundary layers less than a few tens of kilometers can be maintained over vertical distances of several hundred kilometers, even for plume temperatures only 100¿C above the temperature of the ambient mantle. The velocity boundary layers of upwelling plumes can extend to much larger lateral distances, e.g., several hundred kilometers, especially for excess plume temperatures of 100¿C. These conclusions are valid for both olivine (non-Newtonian) nad Newtonian plumes. Olivine plumes generally have upward velocities in excess of 10 cm/yr, except for large values of the activation volume, say, 30 cm3 mol-1, in which case the velocities are only a few centimeters per year. The temperature dependence of the viscosity plays a significant role in the structure of these boundary layer flows. Non-Newtonian olivine plumes rise faster and are narrower than the Newtonian ones. This general conclusion must be taken with caution, since Newtonian rheological parameters are uncertain. An increase in activation volume broadens the olivine plumes and lowers their velocities. Viscous heating is unimportant in these flows. Stresses are generally found to lie in the range 1--10 bars. Lowering the plume temperature relative to that of the ambient mantle induces a thickening of the thermal and viscous boundary layers and an increase in the thickness of the viscous boundary layer relative to that of the thermal one. Olivine and Newtonian plumes thicken according to the 1/6 and 1/4 power, respectively, of the vertical distance from their depth of origin.