A field method is proposed for determining the three-dimensional hydraulic conductivity tensor and specific storage of an anisotropic porous or fractured medium. The method, known as cross-hole testing (to distinguish it from conventional single-hole packer tests), consists of injecting fluid into (or withdrawing fluid from) packed-off intervals in a number of boreholes and monitoring the transient head response in similar intervals in neighboring boreholes. The directions of the principal hydraulic conductivities need not be known prior to the test, and the boreholes may have arbitrary orientations (e.g., they can all be vertical). An important aspect of the proposed method is that it provides direct field information on whether it is proper to regard the medium as being uniform and anisotropic on the scale of the test. The first paper presents theoretical expressions describing transient and steady state head response in monitoring intervals of arbitrary lengths and orientations, to constant-rate injection into (or withdrawal from) intervals having similar or different lengths and orientations. The conditions under which these intervals can be treated mathematically as points are investigated by an asymptotic analysis. The effect of planar no-flow and constant-head boundaries on the response is analyzed by the theory of images. The second paper describes the field methodology and shows how the proposed approach works in the case of fractured granitic rocks.