The writer's theory of surface instability of an elastic body under initial stress in finite strain is extended to anisotropic elasticity. The general characteristic equation for surface instability is derived. In addition, the surface deflexion under a normal load is evaluated for the subcritical case of initial stress. The analysis includes the case in which gravity is taken into account. It is found that for a certain value of the initial stress the surface behaves as if the solid were a fluid, and surface loads sink to a depth at which they are supported by buoyancy forces only.