The Bailey-BRE Method is a simplified design approach that facilitates the use of a tensile membrane action design philosophy for composite floors under fire conditions. The method requires the division of a composite floor into rectangular slab panels, composed of parallel unprotected composite beams in their interior parts, supported vertically by protected composite edge beams. Enhanced slab capacities are obtained after the unprotected beams have lost significant strength, by allowing large deflections of the slab in biaxial bending. The use of tensile membrane action generates significant cost savings in composite structures, as a large number of floor beams can be left unprotected. However, the protected beams which provide vertical support to the edges of panels lose strength under the combined effects of thermal degradation and the increased loading due to biaxial bending, and this has the potential to cause panels to lose structural stability altogether. It is therefore imperative to investigate what constitutes adequate vertical support and the detrimental effects of inadequate vertical support on tensile membrane action of composite slabs in fire. This paper reports on a study of this effect, and puts forward some simple recommendations to avoid loss of stability of composite floors designed by this method.