We consider steady flow of water in a confined aquifer toward a fully penetrating well of radius rw (Figure 1). The hydraulic conductivity K is modeled as a three-dimensional stationary random space function. The two-point covariance of Y=ln(K/KG) is of axisymmetric anisotropy, with I and Iv, the horizontal and vertical integral scales, respectively, and KG, the geometric mean of K. Unlike previous studies which assumed constant flux, the well boundary condition is of given constant head (Figure 1). The aim of the study is to derive the mean head ⟨H⟩ and the mean specific discharge ⟨q⟩ as functions of the radial coordinate r and of the parameters &sgr;2Y, e=Iv/I and rw/I. An approximate solution is obtained at first-order in &sgr;2Y, by replacing the well by a line source of strength proportional to K and by assuming ergodicity, i.e., equivalence between H¿,q¿, space averages over the vertical, and ⟨H⟩,⟨q⟩, ensemble means. An equivalent conductivity Keq is defined as the fictitious one of a homogeneous aquifer which conveys the same discharge Q as the actual one, for the given head Hw in the well and a given head H¿ in a piezometer at distance r from the well. This definition corresponds to the transmissivity determined in a pumping test by an observer that measures Hw, H¿, and Q. The main result of the study is the relationship (19) Keq=KA(1-&lgr;)+Kefu&lgr;, where KA is the conductivity arithmetic mean and Kefu is the effective conductivity for mean uniform flow in the horizontal direction in the same aquifer. The weight coefficient &lgr;10, &lgr; has the simple approximate expression &lgr;*=ln(r/I)/ln(r/rw). Near the well, &lgr;≂0 and Keq≂KA, which is easily understood, since for rw/I≪1 the formation behaves locally like a stratified one. In contrast, far from the well &lgr;≂1 and Keq≂Kefu, the flow being slowly varying there. Since KA>Kefu, our result indicates that the transmissivity is overestimated in a pumping test in a steady state and it decreases with the distance from the well. However, the difference between KA and Kefu is small for highly anisotropic formations for which e≪1. A nonlocal effective conductivity, which depends only on the heterogeneous structure, is derived in Appendix A along the lines of Indelman and Abramovich <1994>. ¿ American Geophysical Union 1996