The mechanistic model of Taitel and Dukler [1] has previously been reported to exhibit a region in which three solutions exist for the height of the gas-l quid interface in the stratified/wave flow regime. Most laboratory studies have not dealt with flow rates in the ranges where the multiple solutions occur An experimental study, has been carried out at the University of Calgary to obtain such data. The object of this work is to review the relevant theory, investigate situations where theory suggests that multiple solutions should exist, and attempt,to show whether or not such solutions do physically exist.