Velocity covariance of seepage flow is the essential quantity in understanding the uncertainty of groundwater flow and contaminant transport in heterogeneous porous media. Nevertheless, a closed-form analytical expression is available only for first-order analysis. These available expressions are limited to some specific correlation functions of natural log hydraulic conductivity. The present paper develops a general method for obtaining the first-order velocity covariance for any statistically isotropic log-hydraulic conductivity correlation function. The general analytical expressions are derived for both two and three dimensions. The results are demonstrated for several frequently used correlation functions. ¿ 1999 American Geophysical Union