The paper describes the phenomenon of drop suspension above an air-blown porous surface, which is similar to the well-known levitation of a drop evaporating above a hot plate (‘spheroidal state’ or the Leidenfrost phenomenon). It has been shown that the basis of this similarity is the close analogy between the hydrodynamic mechanisms of drop suspension. Together with the viscous mechanism, the effect of gas- or heat-flow choking under the drop plays an important role here. The latter conditions the threshold character of the above phenomena. A mathematical model of cool- and hot-drop suspension is offered which does not contain any a priori assumptions about the drop form and can be applied to the critical range of parameters. An approximation has also been considered in which the bottom of the drop is assumed to be flat, which allows us to carry out an analysis within a wide range of parameters. The simplest version of this approximation is a disk model, where the problems considered are found to be similar. This version allows analytical solution. The model developed has been verified in a ‘cool’ experiment. The theoretical and experimental data have been shown to be in qualitative (and in some respects in quantitative) agreement.