A closed-form solution is presented for the long-term deformation and excess pore pressures in a saturated, poroelastic half-space, caused by withdrawal of pore fluid at a constant rate from a point sink located at a finite depth below the surface. The soil is assumed to have isotropic elastic properties but is assumed to be transversely isotropic with respect to its flow properties. Pore pressure and subsidence profiles have been evaluated for a number of practical cases.