Subsidence over an underground cavity is modeled by assuming the subsiding region to be an infinitely long elastic layer that rests on a rigid base and deforms under its own weight into an opening under its lower surface. An approximate analytic solution based on Fourier transform methods is found for vertical displacements of the ground surface and the roof of the opening when the layer thickness is much greater than the width of the opening. This model differs from previous analytic models in allowing both the ground surface and cavity roof to be traction-free. The shape of the surface subsidence trough is found to be controlled by the ratio of the layer thickness to the width of the opening; as the value of this ratio decreases the subsidence trough narrows and a peripheral ridge forms.