It is widely known that oil droplets can decrease the stability of aqueous films and foams. While less widely recognized, it has also been observed that oil droplets can, under certain circumstances, increase the stability of foams, especially if they are caught in the Plateau borders. In this paper, how the oil droplet deforms and is, in turn, deformed by the Plateau border is modeled using Surface Evolver. The two dimensionless parameters that affect these shapes are the size of the oil droplet relative to the Plateau border and the ratio of the oil-water interfacial tension to the air-water interfacial tension. The calculated pressures in all the phases were used to obtain the pressure exerted on the oil-water-air pseudoemulsion film, which allows the factors that influence the stability of these droplets in the Plateau border to be investigated. The final section of the paper demonstrates that the presence of an oil droplet in a Plateau border can have a major influence on the drainage of the aqueous phase along the Plateau border. This retardation of the flow would result in the oil droplets in the Plateau borders increasing the stability of foams in which they are found.