Clay soils, as a result of shrinking-swelling, usually have a capillary crack network. The objective of this presentation is to develop a physically based model of the hydraulic conductivity of a swelling clay matrix with interaggregate capillary cracks only. It is based on a number of assumptions relating in the main to the geometrical characteristics of the capillary crack network and the use of the cubic law for water flow in a water-filled slit. The key assumption speaks about the contraction of the interaggregate capillary crack volume in a drying but saturated clay matrix. The expression for vertical hydraulic conductivity of the network of cracks of width is determined by network tortuosity and specific length of crack traces at a horizontal cross section. To check the model, we compared the available data on the hydraulic conductivity of an Israeli clay soil with model predictions of the hydraulic conductivity of an interaggregate capillary crack network in combination with the independent predictions of hydraulic conductivity of the soil matrix available in literature. This comparison demonstrated satisfactory agreement. ¿ 2001 American Geophysical Union