The design of an externally pressurized air bearing for which the gap can only take two given values is optimized in such a way that the net lift force it can achieve is maximum. The distribution of the gap is assumed to be periodic in the direction perpendicular to the main air flow with a period small enough so that the problem can be treated as one dimensional via the process of homogenization. The optimization analysis is subject to the constraint of a given gap volume which can be justified for stability reasons. An analytical solution is proposed within the framework of Reynolds' equation which shows a large improvement when compared with the typical step bearing at low gap volume. © 1990 Taylor & Francis Group, LLC.