Axisymmetric spherical shell numerical simulations of mantle convection were carried out to investigate the influence of two end-member surface stress conditions: stress-free and rigid. These correspond approximately to a subducting or a rigid lithosphere and can be seen as end-member models of the surface of Venus. Our model assumed an effective Rayleigh number of 3¿106, similar to that for Earth, and included uniform internal heating and depth-dependent thermal expansivity α and thermal conductivity k. The simulations utilized a Newtonian viscosity which was constant or varied with depth and/or temperature. We show how the temperature, speed and vorticity fields change qualitatively and quantitatively with surface temperature, surface stress condition, internal heating and viscosity distribution. Among the significant results, we find that a rigid lid and viscosity which increases with depth both promote steady large-scale circulation with smaller-scale circulation in the upper mantle. ¿ American Geophysical Union 1992