In this study, covariance functions of specific discharge for both one-dimensional and two-dimensional flows in a semiconfined aquifer were derived with mean flow parallel to the formation bedding. Spectral theory was used to analyze a unidirectional mean flow field of infinite extent which is perturbed by one- and two-dimensional statistically homogeneous hydraulic conductivity field. Relatively simple closed-form analytical expressions requiring only some numerical integration for two-dimensional flows were obtained for the longitudinal and transverse components of specific discharge covariance. The spatial, statistical structure of the specific discharge field was investigated in terms of the leakage factor and spatial structure of hydraulic conductivity field. ¿ 1998 American Geophysical Union