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The goal of this study is to develop a mathematical model using the existing source and Green’s functions for a horizontal well completed in an oil reservoir at steady state flow period for anisotropic reservoirs, where the reservoir is bounded by an edge and bottom constant pressure boundaries for the interpretation of pressure responses in the reservoir based on dimensionless pressure and derivatives.Using reservoir and well parameters as well as the variation in permeability in different directions, Excel software was used to investigate which set of reservoir (anisotropic ratios) and well parameters would prolong productivity before steady state set in. Results show that higher vertical permeability will produce much crude in less time before the encroachment of external fluid. Consequently, the production potential of the horizontal well will be reduced with time.The use of longer well lengths will tend to hasten the encroachment of unwanted fluid into the wellbore as wells were already feeling boundary effects beyond tD=1 while shorter well lengths will prolong production. Dimensionless pressure increases as reservoir pay thickness increases, delaying steady-state conditions. The higher the distance from the bottom of the reservoir in dimensionless variable (ZwD), the larger the dimensionless pressure and derivative and hence the better the productivity of the well and reservoir before the setting in of external reservoir fluid.