Two dimensional thermal convection of a fluid layer overlayed by a conductive lid is studied. Lateral thermal conductivity variation is assumed within the rigid lid, in order to see how an increase of the thermal conductivity within the lithosphere can stabilize a downwelling plume beneath it. Calculations are performed for a constant viscosity fluid with Rayleigh numbers (Ra) up to 4¿105. Different lid thicknesses (Δ) and thermal conductivity (k) values are considered. The numerical results reveal a coupling between the zone of high thermal conductivity and the downwelling plumes. The adjustment time of the convective circulation decreases when the values of parameter (Ra, Δ, k) increase. The lowest value for the adjustment time (500 My), is obtained for Ra=4¿105. The calculations suggest that an increase of the effective thermal conductivity causes the anchoring of downwelling mantle jets below primitive continental nuclei. The presence of such sinking plumes attached to the cratonic lithosphere may protect them against disruption by mantle flow. The increase in the effective thermal conductivity of the cratonic lithosphere is attributed to thermal conductivity anisotropy of olivine crystal. Such a mechanism can explain the stability of old continental sheilds. ¿ American Geophysical Union 1988