A new numerical procedure for modeling single phase miscible dispacement in a porous medium is presented. This model is based upon a material balance that is similar to that which is used to derive the differential equations that govern single phase miscible displacement. Since the procedure is defined in terms of a material balance, the data structures arising in a computational implementation are compatible with those that are present in finite difference models of miscible displacement. This procedure obeys a maximum principle due to the upstream weighting of the convective transport terms. This new procedure does not exhibit the grid orientation effect present in the five point finite difference models of this process.