Laboratory experiments and numerical calculations are used to study how a laminar thermal plume deforms and penetrates a buoyant and viscous layer, which serves as an analog for continental lithosphere. The viscosity contrast between the two liquids and the buoyancy ratio B (the ratio between the intrinsic chemical density contrast and the thermal density contrast due to temperature differences) are varied by 3 orders of magnitude and 1 order of magnitude, respectively. The manner of plume-lithosphere interaction is not sensitive to the viscosity contrast, which sets the timescale for displacement of the interface, and depends mostly on the B value, which sets the magnitude and shape of interface deformation. Heating of the upper layer by plume material plays an important role. For B > 0.6, plume material spreads beneath the interface and applies a buoyancy force which deforms the interface. For B < 0.6, true plume penetration into the upper layer occurs with a significant vertical velocity component. With time, the upper layer may become unstable and develop an active upwelling which entrains material from the lower layer. Approximate scaling laws allow prediction of interface displacement as a function of time for the whole parameter range studied. Applied to the continental lithosphere, these results show that true plume penetration through Archean lithosphere requires thermal anomalies larger than 300 K corresponding to buoyancy fluxes in excess of those determined today for the Hawaiian plume. Mantle plumes have different effects on lithospheres of different ages and composition, which precludes diagnosis of a single typical plume signature.