Modem utility-scale wind turbine towers are typically conical steel structures that could also be used to store gaseous hydrogen in what we have termed a hydrogen tower. This paper examines potential technical barriers to this technology and identifies a minimum cost design. We discovered that hydrogen towers have a "crossover pressure" at which the critical mode of failure crosses over from fatigue to bursting. The crossover pressure for many turbine towers is between 1.0 and 1.5 MPa (approximately 10-15 atm). The hydrogen tower design resulting in the least expensive hydrogen storage uses all of the available volume for storage and is designed at its crossover pressure. An 84-m tall hydrogen tower for a 1.5-MW turbine would cost an additional $83,000 (beyond the cost of the conventional tower) and would store 940 kg of hydrogen at 1.1 MPa of pressure. The resulting incremental storage cost of $88/kg is approximately 30% of that for conventional pressure vessels. Published by Elsevier Ltd on behalf of the International Association for Hydrogen Energy.