The simulation of oil displacement by steam injection is affected by the orientation of the grid. Under certain situations vastly different results are obtained when grid lines are parallel or diagonal to the line joining an injector-producer pair in a fivespot flood pattern. The same problem exists in the displacement of oil by water under conditions of unfavorable mobility ratio. Several approaches have been used by investigators to reduce the effect of grid orientation. Three of these are investigated in this paper: (1) use of a nine-point finite-difference operator as opposed to a five-point finite-difference operator, (2) use of the two-point upstream mobility instead of a single-point, and (3) use of harmonic total mobility average for calculation of flow across a boundary. A compositional, three-phase, two-dimensional steam model was developed to investigate the grid orientation problem during steam displacement. A realistic steam displacement problem for a highly viscous oil reservoir was selected for detailed study. The effects of grid orientation on important primary variables and recovery performance curves are presented for this problem. It is shown that, at least for the problem considered, the nine-point scheme alleviates the effect of grid orientation, while the two-point upstream mobility and the harmonic total mobility approaches aggravate the problem. It is also shown that use of the two-point upstream mobility is not appropriate for thermal process simulation. The present model does not suffer from the "bullet-like" displacement front reported by other investigators. The test problem was chosen to maximize the effect of grid orientation.