There has been some recent controversy over the precise nature of the conditions to be imposed at the core-mantle boundary when the Earth suffers a static deformation. We here define static deformation by requiring the fluid core to be in hydrostatic equilibrium both before and after the deformation, and then show how to determine the fluid response in terms of the gravitational potential and normal stress, without reference to particle displacement. The core-mantle boundary is modelled by a thin transition layer between the solid and the fluid in which the ridigity drops to zero. A careful examination of the jump conditions across the transition layer leads to the conclusion that the variables y1, y2 and y6 as defined in the solid are all discontinuous.