The sensitivity of a numerical steamflooding model with respect to mobility weighting is examined in depth. Three numerical discretization procedures are used in this investigation: a new numerical scheme, a five point finite difference method, and a procedure which, under certain assumptions, is equivalent to that introduced by McCracken and Yanosik. Three mobility weighting schemes are investigated. The first approach studied is upstream mobility weighting. The second method investigated uses harmonic total mobility weighting and upstream weighting of fractional flow terms. The approach introduced in this investigation uses the kinematic viscosity in the total mobility and fractional flow terms. Computational results for a simulated steam drive indicate that this new mobility weighting approach is superior to the other two mobility weighting schemes. In particular, the steam displacement model formed from t he combination of this new mobility weighting approach and the McCracken and Yanosik discretization procedure is shown to produce realistic simulation of an inverted seven spot pattern under a continuous steam drive.