Numerical studies of establishment of selective withdrawal from a point sink of a linearly stratified Boussinesq fluid in a reservour of uniform depth have been performed. The flow, which is axisymmetric with respect to the vertical axis passing through the point sink, is mainly characterized by the Froude number (Fr). When the Froude number is small, the columnar disturbance modes propagate upstream in the same manner as in the line sink flow (two dimensional) case and that the selective withdrawal is established. We have found, however, the major difference in the large Froude number flows, where in the two dimensional case the columnar disturbances can not propagate upstream, while in the axisymmetric case these can propagate upstream for any finite Froude number except infinity. Amplitude of these columnar disturbances relative to a basic current velocity becomes smaller as the Froude number increases so that the selective withdrawal ceases to occur at Fr=1.5.