Abstract Two appendices describe the mathematical and algebraic details that led to the formulas provided in the text of this paper. Appendix A presents the general solution, and briefly describes the techniques for deriving simple, closed form expressions for single, double, and triple sums of infinite series. Appendix B describes these procedures in a little more detail, and also indicates certain methods for averaging the variable wellbore pressures in the general anisotropic cases. Uniform Flux Boundary Condition For well problems similar to the one treated in this paper, a uniform flux, or a uniform pressure is commonly imposed as a boundary condition at the well surface. Recognizing that neither is entirely correct, the question that has been debated is whether one is preferable to the other, or whether both give satisfactorily accurate solutions. Muskat(7) shoved that the uniform flux boundary condition gives values accurate to 0.5 percent. We also investigated the implication of the uniform flux assumption. We used our exact solution (Equations A1–A3) and computed the wellbore pressure, pwf at various locations y along the well length L. We did this for isotropic and anisotropic systems where the wells were located at the center, or away from the center. For the anisotropic runs the value of kz was equal to, or twice as large as, that of ky, and was ten times that of kz. Also L/b-0.5. We found that the maximum variation in pwf values was 7 psi for the worst case. This was the anisotropic case with kx=2ky, kx=10kz, and the well was located away from the center. For the other cases, the variation was less than 3 psi. Since one expects pwf to be of the order of several hundred, if not thousand pounds, we concluded that the uniform flux assumption resulted in approximately uniform pressure. Therefore, we expect a uniform pressure boundary condition to result in approximately uniform flux. Thus we concluded that these two boundary conditions lead to approximately the same solution. Treatment of Anisotropy As described in some detail in Appendix B, permeability anisotropy introduces angular dependence of wellbore pressures in the vertical (x=z) plane. This angular dependence can be removed by an averaging procedure, and the averaged pressure is identical to that of an equivalent isotropic reservoir with scaled dimensions. It is also indicated in Appendix B that this average pressure is the actual pressure measured at an angle θ given by: θ=are tan (kz/kx)1/4 from the x-axis. In much of the subsequent work in this paper, computations and derivations will be performed assuming homogeneity and isotropy. However, the final results will be expressed in terms of the permeabilities (kx, ky, kz) for the general anisotropic reservoir. Furthermore, it will be assumed that the pressures are computed at an angular position of θ=[are tan(kz/kx)1/4] on the well perimeter in the general anisotropic cases.