In some places, there is strong evidence that the lower continental crust has flowed so as to smooth out variations in crustal thickness caused by differential crustal extension or shortening. In order to better understand the processes involved, we investigate the behavior of a fluid layer over a fluid half-space to see how such a system responds to the deformation of its upper and lower boundaries. This simple system can be used to study both the decay of crustal thickness contrasts and the behavior of a thin lithospheric sheet. The changing response of the system to variations in density and viscosity contrasts and to different boundary conditions imposed on the fluid interface can easily be studied analytically. The most important results are that variations in crustal thickness on a wavelength of a few times the thickness of the flowing channel will decay quickest and that large lateral variations in crustal thickness cause the fluid to develop a steep front, which may cause a topographic step above it at the Earth's surface. Deformation within the channel will be principally by simple shear. The clear association of lower crustal flow with regions of thickened crust and magmatic activity suggests that both can reduce the viscosity of the lower crust to levels at which flow can occur. The smoothing of crustal thickness contrasts leads to differential vertical motions, and is thus a method by which substantial tilting can occur without faulting. This differential uplift may be responsible for rotating and exhuming some of the detachment faults in metamorphic core complexes in the Basin and Range province of the western United States. It is also a method of causing structural inversion in basins that does not require the reactivation of normal faults as thrusts or reverse faults. ¿ 2000 American Geophysical Union