The purpose of this study is to develop a mathematical formulation and the equations for use in a numerical model that will simulate the performance of a steamflood applied to a waterflooded reservoir. Through the application of such a process the incremental oil recovery can hopefully be determined as accurately as possible. An accurate prediction is critical in determining the economic feasibility of such an operation. Furthermore, such a model will present the opportunity to evaluate the effects of parametric changes on the recovery efficiency. Also critical to the study is the consideration of the high water saturations due to the precession of the waterflood. The effects on the development and movement of the steam zone are examined as well as the effects on the formation of steam-override. For the study, the van Meurs and van der Poel theory is adopted which is capable of defining water saturations at any stage of a waterflood project. The water saturation profile thus obtained is then defined as the initial water saturation profile in the reservoir at the onset of the steamflood. A general analytical solution is presented which follows closely the Yortsos and Gavalas upper bounds theory. The solution yields two upper bounds for the volume of the steam zone for a three-dimensional geometry. The results for steam zone volume growth are then used in calculating the incremental oil recovery based on the Myhill and Stegemeier oil recovery equations. A tentative procedure for a numerical model solution is also presented only to be detailed in another study.