The plant hormone auxin controls root epidermal cell development in a concentration-dependent manner. Root hairs are produced on a subset of epidermal cells as they increase in distance from the root tip. Auxin is required for their initiation and continued growth, but little is known about its distribution in this region of the root. Contrary to the expectation that hair cells might require active auxin influx to ensure auxin supply, we did not detect the auxin-influx transporter AUX1 in root-hair cells. A high level of AUX1 expression was detected in adjacent non-hair cell files. Non-hair cells were necessary to achieve wild-type root-hair length, although an auxin response was not required in these cells. Three-dimensional modelling of auxin flow in the root tip suggests that AUX1-dependent transport through non-hair cells maintains an auxin supply to developing hair cells as they increase in distance from the root tip, and sustains root-hair outgrowth. Experimental data support the hypothesis that instead of moving uniformly though the epidermal cell layer, auxin is mainly transported through canals that extend longitudinally into the tissue.