The maximum effective hole-diameter mathematical model describing the flow of slightly compressible fluid through a commingled reservoir was solved rigorously with consideration of wellbore storage and different skin factors. The exact solutions for wellbore pressure and the production rate obtained from layer j for a well production at a constant rate from a radial drainage area with infinite and constant pressure and no flow outer boundary condition were expressed in terms of ordinary Bessel functions. These solutions were computed numerically by the Crump's numerical inversion method and the behavior of systems was studied as a function of various reservoir parameters. The model was compared with the real wellbore radii model. The new model is numerically stable when the skin factor is positive and negative, but the real wellbore radii model is numerically stable only when the skin factor is positive.