There has been a growing interest in the use of two-dimensional mathematicalmodels to simulate the transient behaviour of oil and gas fields. Until very recently, the standard numerical technique used the alternating direction implicit procedure (ADIP) to integrate the basic partial differential equation describing flow through porous media. However, the computational problem, evenon high-speed computers, remained a form idable one. A new method for solving the conduction equations, first suggested by Saul'ev and later extended by Larkin, makes ingenious use of the known boundary conditions to permit an explicit point-by-point sequential evaluation of all interior grid points. A reverse sweep is used to minimize the over-all errors. The method, which may becalled an alternating direction explicit procedure (ADEP), combines thestability of the implicit methods with the computational ease of the explicit methods. By examining the structure of the computational models and noting their physical significance, it is shown that ADEP is a logical extension of ADIP and should have about the same accuracy. The new method is applied to anexample problem involving a volumetric under saturated oil reservoir, mathematically represented by several hundred grid points. The results indicatea possible order of magnitude saving in computer time for problems of this typeas compared to an ADIP solution. This suggests that three-dimensional models might now very well be practicable. Introduction The present paper is a preliminary report on a new numerical method, firstproposed by Saul'ev (1) and later extended by Larkin (2), for solving the basicpartial differential equation describing the flow of a slightly compressiblefluid through porous media. As it involves an alternating direction explicitprocedure, it may be referred to as ADEP. Because of limitations of computational machinery and costs, existingmethods have been largely limited to the two-dimensional case. The mostefficient of these methods is the alternating direction implicit procedure, or ADIP, developed by Peaceman and Rachford (3). By examining the proposed methodin the mathematical context of earlier computational models, we can drawcertain, hopefully valid conclusions about its accuracy, its stability and itscalculational requirements. No attempt will be made here to give formalmathematical proofs of stability or to present a detailed error analysis -important considerations which have been examined elsewhere (4).