Abstract: The max effective hole-diameter mathematical model describing flow of slightly compressible fluid through a three layers crossflow reservoir is solved rigorously with consideration of wellbore storage and different skin factors.The exact solutions for wellbore pressure and the production rate from layer j obtained for a well producing at a constant rate from a radial drainage area infinite,no flow and constant pressure outer boundary condition are expressed in terms of ordinary Bessel functions.The numerical computation of these solutions is made by Crump numerical inversion method and the behavior of the systems is studied as a function of various reservoir parameters.The new model is compared with the real wellbore radii model.The new model is numerically stable when the skin is positive and negative.The real wellbore radii model is numerically stable when the skin is positive.Because the curves explicitly include skin factor and other reservoir parameters,the techniques is expected to be more accurate than the real wellbore radii model.The automatic history matching technique has made it possible to accurately determine individual layer properties and wellbore parameters.