The max effective hole-diameter mathematical model describing flow of slightly compressible fluid through two-layer reservoir with crossflow is solved rigorously. The model considers all layers open to a single well that flows at a constant wellbore pressure. The effect of formation damage is included in the model. The exact solutions are expressed in terms of ordinary Bessel functions by using the method of Laplace transform. The numerical computation of these solutions is made by Stehfest numerical inversion method. The new model is numerically stable when the skin is positive and negative. The effect of the reservoir parameters such as permeability, vertical permeability, skin, outer boundary conditions and storativity on the layer production rate and total rate were investigated. These results can be used to analyse unsteady flow test of production under the constant pressure condition.

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