Summary: Numerical results are presented for various configurations that may be described as axisymmetric floating drops. In each case the drops are constructed by matching solutions of the differential equations for the axisymmetric capillary surfaces to solve a free boundary problem. These include both “heavy” and “light” drops in which the density of the fluid in the drop is either larger or smaller than that of the reservoir on which it rests. The reservoir may be either infinite or contained in a finite container. Of particular interest are heavy drops which have multiple necks reminiscent of classic results of Kelvin for pendent drops.