Numerical experiments on steady state thermal convection in a cylindrical geometry have been carried out to identify the conditions necessary for plumes to occur in the mantle. Internally and base-heated flows with both constant and variable diffusion creep viscosity have been considered. These experiments show that plumes occur only for base-heated variable viscosity flows. Plumes are examined as a possible mode of convection in the upper mantle above 700 km, since it is in this region of the mantle that base heating should be most dominant. The consequences of an upper mantle plume under Hawaii are discussed in terms of available geological and geophysical observations, and good agreement is found. Plumes also explain the shape of the geotherm under South Africa derived by pyroxene geothermometry.